Mathematics › Sequence & Series
Sequence & Series Questions
638 questions across 7 subtopics — with step-by-step solutions.
A.G.P.(7)
- Match the following series sums.List - ILi... | Mathematics | TestHub
- The sum of the infinite series 1 + \frac{4... | Mathematics | TestHub
- If , then the value of is : | Mathematics | TestHub
- Find the positive integer n satisfying \su... | Mathematics | TestHub
- If 1+4 x+7 x^{2}+10 x^{3}+\cdots=35 / 16 f... | Mathematics | TestHub
- If the number of coins earned in the n th... | Mathematics | TestHub
- The sum of the series \frac{x}{1-x^{2}}+\f... | Mathematics | TestHub
A.P.(197)
- Let a_1, a_2, \ldots, a_n be an arithmetic... | Mathematics | TestHub
- Let S_n denote the sum of the first n term... | Mathematics | TestHub
- If the sum of the first n terms of an A.P.... | Mathematics | TestHub
- Let S_n denote the sum of the first n term... | Mathematics | TestHub
- The sum of integers from 1 to 100 that are... | Mathematics | TestHub
- If are in A.P. then equals | Mathematics | TestHub
- Let be a polynomial function of second deg... | Mathematics | TestHub
- Let be the rth term of an A.P. whose first... | Mathematics | TestHub
- Let be terms of an A.P. If , then equals | Mathematics | TestHub
- Paragraph:Let denotes the sum of the first... | Mathematics | TestHub
- Paragraph:Let denotes the sum of the first... | Mathematics | TestHub
- Let be real numbers satisfying and for . I... | Mathematics | TestHub
- A person is to count 4500 currency notes.... | Mathematics | TestHub
- If the sum of the first terms of is equal... | Mathematics | TestHub
- Let be an arithmetic progression with and... | Mathematics | TestHub
- A man saves Rs. 200 in each of the first t... | Mathematics | TestHub
- If the A.M. between and terms of an A.P. i... | Mathematics | TestHub
- Let be terms on A.P. If then equals | Mathematics | TestHub
- If times the term of an with non zero comm... | Mathematics | TestHub
- Given sum of the first terms of an A.P. is... | Mathematics | TestHub
- If . are in A.P. such that , then the sum... | Mathematics | TestHub
- Ifare positive numbers inand,andare also i... | Mathematics | TestHub
- Let be an A.P, such that . Then is equal to: | Mathematics | TestHub
- The sum of the first 20 terms common betwe... | Mathematics | TestHub
- If are in A. P., then is equal to | Mathematics | TestHub
- The number of terms in anis even, the sum... | Mathematics | TestHub
- Given an A.P. whose terms are all positive... | Mathematics | TestHub
- Suppose that all the terms of an arithmeti... | Mathematics | TestHub
- Let the sum of the first three terms of an... | Mathematics | TestHub
- If a, , and are in A.P. and also a a are i... | Mathematics | TestHub
- Let,be in A.P. If, then the sum of its fir... | Mathematics | TestHub
- The fourth term of an A.P. is three times... | Mathematics | TestHub
- The numbersandform first three terms of an... | Mathematics | TestHub
- The sides of a right-angled triangle are i... | Mathematics | TestHub
- Ifandare two A.P.s such that, thenis equal to | Mathematics | TestHub
- If and are two A.P's such that and , then... | Mathematics | TestHub
- Letbe the set consisting of the firstterms... | Mathematics | TestHub
- Letdenote the sum of the firstterms of an.... | Mathematics | TestHub
- If the sum and product of the first three... | Mathematics | TestHub
- Let the sum of the firstterms of a non-con... | Mathematics | TestHub
- Letbe anwithThen, the common difference of... | Mathematics | TestHub
- Ifare in A.P. such thatthen the sum of the... | Mathematics | TestHub
- Letdenote the set of all the terms of an i... | Mathematics | TestHub
- Letbe an A.P.,andIfandthenis equal to: | Mathematics | TestHub
- The sum of all two digit positive numbers... | Mathematics | TestHub
- If 19 th term of a non-zero A.P. is zero,... | Mathematics | TestHub
- The sum of all natural numberssuch thatandis | Mathematics | TestHub
- Let. If, thenis equal to : | Mathematics | TestHub
- Ifare inand, thenis equal to : | Mathematics | TestHub
- If the sum of the firstterms of the series... | Mathematics | TestHub
- The number of terms common to the two A.P.... | Mathematics | TestHub
- If the first term of anisand the sum of it... | Mathematics | TestHub
- Five numbers are inwhose sum isand product... | Mathematics | TestHub
- Letbe a given A.P. whose common difference... | Mathematics | TestHub
- If the sum of firstterms of an A.P. ,isthe... | Mathematics | TestHub
- Ifandare the first three terms of an A.P.... | Mathematics | TestHub
- A student read common difference of an A.... | Mathematics | TestHub
- The common difference of theismore than co... | Mathematics | TestHub
- If the, term of an A.P. is, and its, term... | Mathematics | TestHub
- Letbe such that for allandare in A.P., the... | Mathematics | TestHub
- The sum of all odd numbers between 1 and 1... | Mathematics | TestHub
- Letbe an A.P. Ifthenis equal to : | Mathematics | TestHub
- Letbe the sum of the firstterms of an arit... | Mathematics | TestHub
- Ifare in an arithmetic progression, then t... | Mathematics | TestHub
- If the sum of a certain number of terms of... | Mathematics | TestHub
- If the harmonic mean between and be , then... | Mathematics | TestHub
- Letdenote the sum of first-terms of an ari... | Mathematics | TestHub
- A man is walking on a straight line. The a... | Mathematics | TestHub
- Ifare in arithmetic progression andare als... | Mathematics | TestHub
- Letbe the sum of firstterms of an arithmet... | Mathematics | TestHub
- If sum of the firstterms of the serieswher... | Mathematics | TestHub
- Ifandare in arithmetic progression for a r... | Mathematics | TestHub
- Ifandare A.P. andthenis equal to | Mathematics | TestHub
- The series of positive multiples ofis divi... | Mathematics | TestHub
- If and if are in AP, then is equal to | Mathematics | TestHub
- If, whereis an even integer, is an arithme... | Mathematics | TestHub
- For, consider the real valued functionand.... | Mathematics | TestHub
- Different A.P.'s are constructed with the... | Mathematics | TestHub
- Supposebe an arithmetic progression of nat... | Mathematics | TestHub
- Letbe consecutive terms of an arithmetic p... | Mathematics | TestHub
- Letuptoterms anduptoterms be two series. T... | Mathematics | TestHub
- Let be positive consecutive terms of an ar... | Mathematics | TestHub
- Letbe in A.P. Ifand, thenis equal to _____ . | Mathematics | TestHub
- The sum of all those terms, of the arithme... | Mathematics | TestHub
- Letbe the three A.P. with the same common... | Mathematics | TestHub
- For three positive integers,andsuch thatar... | Mathematics | TestHub
- The number ofdigit numbers, that are divis... | Mathematics | TestHub
- Let. be an A.P. If, the productis minimum... | Mathematics | TestHub
- The common term of the series. is | Mathematics | TestHub
- Letbe an A.P. If the sum of its first four... | Mathematics | TestHub
- Let respectively be the sum of terms of wh... | Mathematics | TestHub
- The sum of the common terms of the followi... | Mathematics | TestHub
- Number of-digit numbers that are less than... | Mathematics | TestHub
- The number of-digit numbers, that are divi... | Mathematics | TestHub
- An arithmetic progression is written in th... | Mathematics | TestHub
- Letdenote the sum of the first n terms of... | Mathematics | TestHub
- Let the positive integers be written in th... | Mathematics | TestHub
- Let be in an arithmetic progression of pos... | Mathematics | TestHub
- Letdenote the sum of firstterms an arithme... | Mathematics | TestHub
- Theterm from the end of the progressionis :- | Mathematics | TestHub
- In an A.P., the sixth term. If theis the g... | Mathematics | TestHub
- For , the least value of , for which are t... | Mathematics | TestHub
- Let is neither a multiple of 3 nor a multi... | Mathematics | TestHub
- If the sum of the series is equal to 5 , t... | Mathematics | TestHub
- The number of common terms in the progress... | Mathematics | TestHub
- Ifare in anandare also in an, thenis equal to | Mathematics | TestHub
- A software company sets up number of compu... | Mathematics | TestHub
- Letandbe two arithmetic progressions. Then... | Mathematics | TestHub
- Consider two sets and , each containing th... | Mathematics | TestHub
- The roots of the quadratic equation are an... | Mathematics | TestHub
- Consider an A. P. of positive integers, wh... | Mathematics | TestHub
- Let be the term of an A.P. If for some , a... | Mathematics | TestHub
- If the first term of an A.P. is 3 and the... | Mathematics | TestHub
- Let be in an A.P. such that . If , then n is: | Mathematics | TestHub
- The value of is: | Mathematics | TestHub
- Suppose that the number of terms in an A.P... | Mathematics | TestHub
- The number of 3 -digit numbers, that are d... | Mathematics | TestHub
- For positive integers , if and , then the... | Mathematics | TestHub
- The interior angles of a polygon with n si... | Mathematics | TestHub
- Practice Question | Mathematics | TestHub
- If the sum of the second, fourth and sixth... | Mathematics | TestHub
- Consider two sets and , each containing th... | Mathematics | TestHub
- Let be in an A.P. such that . If , then n is: | Mathematics | TestHub
- If , then the value of is : | Mathematics | TestHub
- then is equal to | Mathematics | TestHub
- If the sum of the first 20 terms of the se... | Mathematics | TestHub
- Let be the term of an A.P. If for some , a... | Mathematics | TestHub
- Let be the term of an A. P.If and , then i... | Mathematics | TestHub
- Practice Question | Mathematics | TestHub
- If the first term of an A.P. is 3 and the... | Mathematics | TestHub
- Let and be the sets consisting of the firs... | Mathematics | TestHub
- The number of terms of an A.P. is even; th... | Mathematics | TestHub
- The sum upto terms, is equal to | Mathematics | TestHub
- Let denote the set of all real numbers. Le... | Mathematics | TestHub
- The sum . upto 20 terms, is equal to | Mathematics | TestHub
- Let be a G. P. of increasing positive numb... | Mathematics | TestHub
- Suppose that the number of terms in an A.P... | Mathematics | TestHub
- Consider an A. P. of positive integers, wh... | Mathematics | TestHub
- Let upto terms. If the sum of the first si... | Mathematics | TestHub
- If , then is equal to : | Mathematics | TestHub
- Let and be the sets consisting of the firs... | Mathematics | TestHub
- Let be an Arithmetic Progression such that... | Mathematics | TestHub
- If \mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm... | Mathematics | TestHub
- Statement-1 : The series for which the sum... | Mathematics | TestHub
- Sum of first hundred numbers common to the... | Mathematics | TestHub
- In a triangle ABC, side lengths a,b,c are... | Mathematics | TestHub
- Eleven arithmetic means are inserted betwe... | Mathematics | TestHub
- Statement 1: If the series itself is an A.... | Mathematics | TestHub
- Positive real numbers a,b,c are in A.P. an... | Mathematics | TestHub
- Let a_{1}, \ldots, a_{n} form an A.P. with... | Mathematics | TestHub
- a, b, c are in A.P. and the points A(a, 1)... | Mathematics | TestHub
- For k=1, \ldots, 50 , let x_{k} be k less... | Mathematics | TestHub
- If \frac{1+3+5+\ldots \text { up to } n \t... | Mathematics | TestHub
- The ratios of the sums of the first n term... | Mathematics | TestHub
- In an A.P. with first term a and common di... | Mathematics | TestHub
- Two sets A and B each have three numbers i... | Mathematics | TestHub
- Two consecutive numbers k, k+1 are removed... | Mathematics | TestHub
- For an A.P. a_{n} , let \alpha=\sum_{r=1}^... | Mathematics | TestHub
- Two sets A and B each have three numbers i... | Mathematics | TestHub
- Along a road lies an odd number of stones... | Mathematics | TestHub
- Three distinct natural numbers in A.P. wit... | Mathematics | TestHub
- The interior angles of a convex polygon fo... | Mathematics | TestHub
- If the side lengths of a right triangle fo... | Mathematics | TestHub
- All terms of an A.P. are natural numbers.... | Mathematics | TestHub
- Let A_{1}, A_{2}, \ldots, A_{m} be arithme... | Mathematics | TestHub
- Let A_{1}, A_{2}, \ldots, A_{m} be arithme... | Mathematics | TestHub
- Four distinct positive numbers a,b,c,d are... | Mathematics | TestHub
- For an A.P. a_{n} , let \alpha=\sum_{r=1}^... | Mathematics | TestHub
- How many terms are common to the first 50... | Mathematics | TestHub
- For k=1, \ldots, 50 , let x_{k} be k less... | Mathematics | TestHub
- Four different integers form an increasing... | Mathematics | TestHub
- Match each item in List I to all applicabl... | Mathematics | TestHub
- Let s_{1}, s_{2}, s_{3}, \ldots and t_{1},... | Mathematics | TestHub
- Distinct integers a, b, c, d are in A.P. a... | Mathematics | TestHub
- The value of n for which a_{n} is maximum is | Mathematics | TestHub
- A sequence has a_{1}=19, a_{9}=99 , and fo... | Mathematics | TestHub
- If the sum of the first 11 terms of an ari... | Mathematics | TestHub
- If 1, \log _{81}\left(3^{x}+48\right), \lo... | Mathematics | TestHub
- Eleven arithmetic means are inserted betwe... | Mathematics | TestHub
- The sequence a_{1}, a_{2}, a_{3}, \ldots,... | Mathematics | TestHub
- All terms of an A.P. are natural numbers.... | Mathematics | TestHub
- The ratios of the sums of the first n term... | Mathematics | TestHub
- If t_{4}=4, t_{5}=5 and t_{n}=2 t_{n-1}-t_... | Mathematics | TestHub
- Let S_{k} denote the sum of the first k te... | Mathematics | TestHub
- Positive terms a_{1}, . ., a_{16} form an... | Mathematics | TestHub
- Two sets A and B each have three numbers i... | Mathematics | TestHub
- If the sum of the first 40 terms of 3+4+8+... | Mathematics | TestHub
- If 1, \log _{81}\left(3^{x}+48\right), \lo... | Mathematics | TestHub
- Four different integers form an increasing... | Mathematics | TestHub
- Four different integers form an increasing... | Mathematics | TestHub
- Distinct integers a, b, c, d are in A.P. a... | Mathematics | TestHub
- If fourth term of a G.P. is 3 , the produc... | Mathematics | TestHub
- If for an A.P. a_{1}, a_{2}, a_{3}, \ldots... | Mathematics | TestHub
- Let a_{n}, n \in N be an A.P. with common... | Mathematics | TestHub
- If \sum_{\alpha=4}^{n+3} 4(\alpha-3)=A n^{... | Mathematics | TestHub
- If a, b, c are in A.P., then (a-c)^{2} equals | Mathematics | TestHub
- Find the sum of all elements of \{\alpha \... | Mathematics | TestHub
G.P.(112)
- The sum of the first two terms of a G.P. i... | Mathematics | TestHub
- Let a_1, a_2, \ldots, a_n, \ldots be a geo... | Mathematics | TestHub
- Fifth term of a GP is 2, then the product... | Mathematics | TestHub
- The value of is | Mathematics | TestHub
- Sum of infinite number of terms of GP is 2... | Mathematics | TestHub
- If and are both in G.P. with the same comm... | Mathematics | TestHub
- Let and . Find a least odd natural number... | Mathematics | TestHub
- In a geometric progression consisting of p... | Mathematics | TestHub
- The first two terms of a geometric progres... | Mathematics | TestHub
- The minimum value of the function subject... | Mathematics | TestHub
- The difference between the fourth term and... | Mathematics | TestHub
- If is positive then the sum to infinity of... | Mathematics | TestHub
- The sum of firstterms of the sequenceis : | Mathematics | TestHub
- The least positive integer such that , is: | Mathematics | TestHub
- In a geometric progression, if the ratio o... | Mathematics | TestHub
- Let be the geometric mean of two positive... | Mathematics | TestHub
- If is the complex cube root of unity, then... | Mathematics | TestHub
- The sum of theand theterms of aisand the p... | Mathematics | TestHub
- Ifis the first term of an infinite geometr... | Mathematics | TestHub
- If is the first term of an infinite G. P w... | Mathematics | TestHub
- Let be a G.P. If then equals : | Mathematics | TestHub
- The sum of an infinite geometric series wi... | Mathematics | TestHub
- Ifandbe three distinct real numbers in G.P... | Mathematics | TestHub
- Ifare the lengths of the sides of a triang... | Mathematics | TestHub
- Letbe theterm of a G.P. of positive terms.... | Mathematics | TestHub
- If the sum of the second, third and fourth... | Mathematics | TestHub
- The producttois equal to: | Mathematics | TestHub
- The sum of the first three terms of is and... | Mathematics | TestHub
- The value ofis __________ | Mathematics | TestHub
- If, thenis equal to | Mathematics | TestHub
- Letbe non-zero distinct real numbers such... | Mathematics | TestHub
- Ifandforthen: | Mathematics | TestHub
- If then is equal to | Mathematics | TestHub
- The greatest positive integerfor whichis a... | Mathematics | TestHub
- Let, be asuch thatand. If, then, is equal to. | Mathematics | TestHub
- If are in G.P., then the area of the trian... | Mathematics | TestHub
- Ifand, then the sum to infinity of the fol... | Mathematics | TestHub
- If the sum of an infinite,isand the sum of... | Mathematics | TestHub
- Consider an infinite geometric series with... | Mathematics | TestHub
- Paragraph: Let , where Consider the geomet... | Mathematics | TestHub
- Paragraph: Let , where Consider the geomet... | Mathematics | TestHub
- In an increasing geometric series, the sum... | Mathematics | TestHub
- Letbe squares such that for eachthe length... | Mathematics | TestHub
- Ifsatisfies the equation, then the value o... | Mathematics | TestHub
- Ifare in a G.P. ,and, thenis equal to _____. | Mathematics | TestHub
- Letbe an increasing geometric progression... | Mathematics | TestHub
- Ifand, thenis equal to | Mathematics | TestHub
- Letbe in geometric progression withand the... | Mathematics | TestHub
- Letdenote thedigit number where the first... | Mathematics | TestHub
- Let. be a G.P. of increasing positive numb... | Mathematics | TestHub
- Let the first term a and the common ratioo... | Mathematics | TestHub
- The 4thterm of GP isand its common ratio i... | Mathematics | TestHub
- Let. be a GP of increasing positive number... | Mathematics | TestHub
- If the sum and product of four positive co... | Mathematics | TestHub
- Let and , be two G.P.s with common ratio a... | Mathematics | TestHub
- If the sum of an infinite GP is 15 and the... | Mathematics | TestHub
- Letandbe two distinct positive real number... | Mathematics | TestHub
- Let be an equilateral triangle. A new tria... | Mathematics | TestHub
- If and , then is equal to | Mathematics | TestHub
- If three successive terms of a G.P. with c... | Mathematics | TestHub
- Let , be an infinite G.P. If and , then is... | Mathematics | TestHub
- If each term of a geometric progressionwit... | Mathematics | TestHub
- If in a G.P. ofterms, the sum of all the t... | Mathematics | TestHub
- In an increasing geometric progression of... | Mathematics | TestHub
- Let be a G. P. of increasing positive numb... | Mathematics | TestHub
- Let be in a geometric progression. are sub... | Mathematics | TestHub
- Let be a G.P. of increasing positive terms... | Mathematics | TestHub
- If the sum of the second, fourth and sixth... | Mathematics | TestHub
- The ratio of sum of first three terms of a... | Mathematics | TestHub
- If the common ratio of a geometric progres... | Mathematics | TestHub
- Numbers a,b,c,d form a G.P. and a-2,b-7,c-... | Mathematics | TestHub
- In a G.P. the product of its first four te... | Mathematics | TestHub
- Let S, P, R be the sum, product, and sum o... | Mathematics | TestHub
- Match each item in List I to all applicabl... | Mathematics | TestHub
- Let S, P, R be the sum, product, and sum o... | Mathematics | TestHub
- If a=\sum_{n=0}^{\infty} x^{n}, b=\sum_{n=... | Mathematics | TestHub
- Positive integers a<b<c form a G.P. with n... | Mathematics | TestHub
- Let A_{1}, A_{2}, \ldots, A_{m} be arithme... | Mathematics | TestHub
- If (1-P)\left(1+3 x+9 x^{2}+27 x^{3}+81 x^... | Mathematics | TestHub
- For an increasing G.P. a_{1}, a_{2}, a_{3}... | Mathematics | TestHub
- If a, b, c are in G.P. and the fractions e... | Mathematics | TestHub
- For \mathrm{r}=1, \ldots, \mathrm{n}, S_{r... | Mathematics | TestHub
- A three-digit number has digits in G.P. Th... | Mathematics | TestHub
- If r>1 and x=a+\frac{a}{r}+\frac{a}{r^{2}}... | Mathematics | TestHub
- The third term of a G.P. is 64. The produc... | Mathematics | TestHub
- The first term of an arithmetic progressio... | Mathematics | TestHub
- Positive integers a<b<c form a G.P. with n... | Mathematics | TestHub
- Find the natural number ' a ' for which \s... | Mathematics | TestHub
- Find the natural number ' a ' for which \s... | Mathematics | TestHub
- Sum of the series 3+5+9+17+33+\ldots .to n... | Mathematics | TestHub
- In a G.P., the first term is 1 . If 4 T_{2... | Mathematics | TestHub
- If a \in(1, e) and \ln a^{2}+\left(\ln a^{... | Mathematics | TestHub
- The first term of an infinite G.P. is 1 an... | Mathematics | TestHub
- If a, b, c are in G.P. and the fractions e... | Mathematics | TestHub
- Statement 1: The sequences 1,2,4,8, \ldots... | Mathematics | TestHub
- Given \mathrm{a}, \mathrm{b}, \mathrm{c} a... | Mathematics | TestHub
- Find the sum to infinity of a decreasing G... | Mathematics | TestHub
- Successive G.P. terms b_{1}, b_{2}, b_{3}... | Mathematics | TestHub
- The first three terms a,b,c of a G.P. have... | Mathematics | TestHub
- Match List I with List II.List IList II(A)... | Mathematics | TestHub
- An infinite geometric series has first ter... | Mathematics | TestHub
- If a_{1}, \ldots, a_{n} are distinct odd n... | Mathematics | TestHub
- An infinite geometric series has first ter... | Mathematics | TestHub
- Let A_{1}, A_{2}, \ldots, A_{m} be arithme... | Mathematics | TestHub
- Statement 1: Starting with an equilateral... | Mathematics | TestHub
- The ratio of sum of first three terms of a... | Mathematics | TestHub
- If a, b, c, d form a G.P., find \left(a^{2... | Mathematics | TestHub
- Assume x, y and z are nonzero real numbers... | Mathematics | TestHub
- If a, b, c, d form a G.P., find \left(a^{2... | Mathematics | TestHub
- Three numbers, the third of which is 4 fro... | Mathematics | TestHub
- The sum of the terms of an infinitely decr... | Mathematics | TestHub
- \alpha, \beta are roots of x^{2}-x+p=0 and... | Mathematics | TestHub
H.P.(35)
- Let a, b, c be in H.P. If a=3 and b=4 , ma... | Mathematics | TestHub
- If non-zero numbers are in H.P., then the... | Mathematics | TestHub
- If in a triangle , the altitudes from the... | Mathematics | TestHub
- If are in H.P., then the expression is equ... | Mathematics | TestHub
- If and terms of H.P. are respectively, the... | Mathematics | TestHub
- Let be in harmonic progression with and .... | Mathematics | TestHub
- If the term of a . . is and the term is th... | Mathematics | TestHub
- If binomial coefficients of three consecut... | Mathematics | TestHub
- Ifandare in, thenis equal to | Mathematics | TestHub
- Let be a harmonic progression with and . T... | Mathematics | TestHub
- Let be in AP and be in HP. If and , then is | Mathematics | TestHub
- If a, b, c are in H.P., then value of \lef... | Mathematics | TestHub
- If H_{1}, \ldots, H_{20} are twenty harmon... | Mathematics | TestHub
- If \log _{a x} x, \log _{b x} x, \log _{c... | Mathematics | TestHub
- If a, b, c are distinct positive reals in... | Mathematics | TestHub
- If a_{1}, \ldots, a_{5} are in H.P., find... | Mathematics | TestHub
- If \log _{a x} x, \log _{b x} x, \log _{c... | Mathematics | TestHub
- Match each item in List I to all applicabl... | Mathematics | TestHub
- The largest positive term of the H.P whose... | Mathematics | TestHub
- If positive a,b,c are in H.P., which state... | Mathematics | TestHub
- The number of integers in the HP is | Mathematics | TestHub
- Nonzero a,b,c are in H.P. Assume every den... | Mathematics | TestHub
- If a, b, c are in H.P., then \frac{a-b}{b-... | Mathematics | TestHub
- If b+c, c+a, a+b are in H.P., what progres... | Mathematics | TestHub
- The pth term of an H.P. is \mathrm{q}(\mat... | Mathematics | TestHub
- Match each item in List I to all applicabl... | Mathematics | TestHub
- If a, b, c are in H.P. and the fractions e... | Mathematics | TestHub
- If are in H.P., and , find the determinant: . | Mathematics | TestHub
- If a, b, c are in H.P., then \frac{a}{b+c}... | Mathematics | TestHub
- Match each item in List I to all applicabl... | Mathematics | TestHub
- If a_{1}, \ldots, a_{5} are in H.P., find... | Mathematics | TestHub
- If H_{1}, \ldots, H_{20} are twenty harmon... | Mathematics | TestHub
- Let x, y, z>1 be in G.P. Which progression... | Mathematics | TestHub
- An H.M. is inserted between the number 1/3... | Mathematics | TestHub
- The value of x . y . z=55 or \frac{343}{55... | Mathematics | TestHub
Means / inequality(80)
- The value of n is | Mathematics | TestHub
- The common difference of the progression \... | Mathematics | TestHub
- The value of m is | Mathematics | TestHub
- The value of \mathrm{G}_{1}+\mathrm{G}_{2}... | Mathematics | TestHub
- Match the following.List - IList - II(P) I... | Mathematics | TestHub
- If , then the difference between the maxim... | Mathematics | TestHub
- Paragraph:Let denote the arithmetic, geome... | Mathematics | TestHub
- If and are positive real numbers such that... | Mathematics | TestHub
- Paragraph:Let denote the arithmetic, geome... | Mathematics | TestHub
- Paragraph:Let denote the arithmetic, geome... | Mathematics | TestHub
- The coefficient of in the expansion of is: | Mathematics | TestHub
- The minimum value of the sum of real numbe... | Mathematics | TestHub
- Find the A.M. of the first ten odd numbers. | Mathematics | TestHub
- The product of positive numbers is unity,... | Mathematics | TestHub
- Column IColumn IIIn , if the magnitude of... | Mathematics | TestHub
- Letbe positive real numbers such thatandTh... | Mathematics | TestHub
- The arithmetic mean of numbers a, is . Wha... | Mathematics | TestHub
- If three positive numbers,andare in A.P. s... | Mathematics | TestHub
- For any three positive real numbersand. If... | Mathematics | TestHub
- If,, thenis equal to | Mathematics | TestHub
- If and are distinct, then b) is greater than | Mathematics | TestHub
- If are positive numbers, then least value... | Mathematics | TestHub
- Letbe the minimum possible value of, where... | Mathematics | TestHub
- Ifarithmetic means (A.Ms) and three geomet... | Mathematics | TestHub
- The minimum value of, whereand, is equal to: | Mathematics | TestHub
- If the arithmetic mean and the geometric m... | Mathematics | TestHub
- Let. If, then the least value ofis | Mathematics | TestHub
- If the minimum value of, is, then the valu... | Mathematics | TestHub
- Consider two G.Ps.andofandterms respective... | Mathematics | TestHub
- Ifarithmetic means are inserted between a... | Mathematics | TestHub
- Letbe in an arithmetic progression, withan... | Mathematics | TestHub
- Letandbe positive real numbers such that.... | Mathematics | TestHub
- Letandbe two arithmetic means andandbe thr... | Mathematics | TestHub
- If and are distinct, then is greater than | Mathematics | TestHub
- If a, b, c are three positive numbers, the... | Mathematics | TestHub
- If n arithmetic means are inserted between... | Mathematics | TestHub
- Match each item in List I to all applicabl... | Mathematics | TestHub
- If x \in R , the numbers 5^{1+x}+5^{1-x},... | Mathematics | TestHub
- Between any two nonzero real numbers a,b,... | Mathematics | TestHub
- If a_{1}, a_{2}, a_{3}, \ldots, a_{n} \in... | Mathematics | TestHub
- If x>0 , then find the greatest value of t... | Mathematics | TestHub
- In an equilateral triangle, a line through... | Mathematics | TestHub
- Statement 1: For positive p,q,r, (\mathrm{... | Mathematics | TestHub
- Match each item in List I to all applicabl... | Mathematics | TestHub
- If one A.M. A and two G.M.s p and q be ins... | Mathematics | TestHub
- If b is the arithmetic mean of positive a,... | Mathematics | TestHub
- For \mathrm{n} \in \mathbb{N} , let A_{n},... | Mathematics | TestHub
- Between 3 and 6 insert ten arithmetic mean... | Mathematics | TestHub
- If a, b, c are positive real numbers such... | Mathematics | TestHub
- Six arithmetic means A_{i} , six geometric... | Mathematics | TestHub
- For \mathrm{n} \in \mathbb{N} , let A_{n},... | Mathematics | TestHub
- If b is the arithmetic mean of positive a,... | Mathematics | TestHub
- For every integer \mathrm{n}>1 , Statement... | Mathematics | TestHub
- Find the minimum of 9 x \sin x+4 /(x \sin... | Mathematics | TestHub
- If G is the G.M. between x and y , then th... | Mathematics | TestHub
- The arithmetic mean of positive \mathrm{a}... | Mathematics | TestHub
- Between the numbers 2 and 20, 8 means are... | Mathematics | TestHub
- Let S_{n}=1+1 / 2+\cdots+1 / n with n>2 .... | Mathematics | TestHub
- Let A_{1}, A_{2}, \ldots, A_{m} be arithme... | Mathematics | TestHub
- Choose the correct statement(s): | Mathematics | TestHub
- If the arithmetic mean of two positive num... | Mathematics | TestHub
- If a_{i}>0 for \mathrm{i}=1, \ldots, \math... | Mathematics | TestHub
- If a b c d=1 where a, b, c, d are positive... | Mathematics | TestHub
- Positive A.P., G.P. and H.P. sequences hav... | Mathematics | TestHub
- The equation a_{8} X^{8}+a_{7} X^{7}+a_{6}... | Mathematics | TestHub
- Choose the correct statement(s): | Mathematics | TestHub
- Statement 1: If a, b, c, d>0 and (a+b+c+d+... | Mathematics | TestHub
- An A.P., G.P. and H.P. have the same first... | Mathematics | TestHub
- Positive x, y, z are in A.P. The minimum o... | Mathematics | TestHub
- Let a, b, c be in A.P. Let p, p^{\prime} b... | Mathematics | TestHub
- If a, b, c are positive real numbers, then... | Mathematics | TestHub
- For positive real a, b, c, d with a b c d=... | Mathematics | TestHub
- The minimum value of \left(8 x^{2}+y^{2}+z... | Mathematics | TestHub
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- For positive real x, y , find the minimum... | Mathematics | TestHub
- If \mathrm{a}, \mathrm{b}, \mathrm{c} \in... | Mathematics | TestHub
- If a, b, c, d>0 such that a+2 b+3 c+4 d=50... | Mathematics | TestHub
- If n arithmetic means are inserted between... | Mathematics | TestHub
- Statement 1: If nonzero real a,b,c satisfy... | Mathematics | TestHub
- For \mathrm{n} \in \mathbb{N} , let A_{n},... | Mathematics | TestHub
Miscellaneous/Mixed(57)
- \left(1^{2}+1\right) 1!+\left(2^{2}+1\righ... | Mathematics | TestHub
- If E=\frac{1}{4} . \frac{2}{6} . \frac{3}{... | Mathematics | TestHub
- If a, b, c are in Arithmetic Progression (... | Mathematics | TestHub
- Let a, b, c be distinct positive integers... | Mathematics | TestHub
- Let and respectively be the maximum ranges... | Mathematics | TestHub
- If where are in A.P. and , then are in | Mathematics | TestHub
- Paragraph:Let denotes the sum of the first... | Mathematics | TestHub
- Suppose four distinct positive numbers and... | Mathematics | TestHub
- If in the expansion of and sum of the bino... | Mathematics | TestHub
- Given a sequence of 4 numbers, first three... | Mathematics | TestHub
- A pack contains n cards numbered from 1 to... | Mathematics | TestHub
- Three positive numbers form an increasingI... | Mathematics | TestHub
- Let a, b, c be positive integers such that... | Mathematics | TestHub
- The value of upto n terms is | Mathematics | TestHub
- If is the of two distinct real numbers and... | Mathematics | TestHub
- LetforSupposeare in Arithmetic Progression... | Mathematics | TestHub
- The sum to terms of the series is | Mathematics | TestHub
- If theandterms of a non-constant arithmeti... | Mathematics | TestHub
- If the arithmetic mean of two numbers and... | Mathematics | TestHub
- Ifare inandandare in, thenandare the lengt... | Mathematics | TestHub
- If are in A.P. and are in G.P. such that a... | Mathematics | TestHub
- Letandbe theandterms respectively of a non... | Mathematics | TestHub
- Letandbe inwith common ratiowhereandIfanda... | Mathematics | TestHub
- The product of three consecutive terms of... | Mathematics | TestHub
- Letbe a sequence of positive integers in a... | Mathematics | TestHub
- There are four numbers of which the first... | Mathematics | TestHub
- Let be the sum of the first term of the se... | Mathematics | TestHub
- Letbe anwith common differenceandbe awith... | Mathematics | TestHub
- If foruptoterms andthen the ordered pairis... | Mathematics | TestHub
- The sum of first four terms of a geometric... | Mathematics | TestHub
- Letbe in arithmetic progression. Let the c... | Mathematics | TestHub
- Three numbers are in an increasing geometr... | Mathematics | TestHub
- Ifandthen : | Mathematics | TestHub
- Consider an arithmetic series and a geomet... | Mathematics | TestHub
- Letandbe in G.P. andbe in A.P., where. The... | Mathematics | TestHub
- If, whereare in A.P. and,, then | Mathematics | TestHub
- In a sequence of terms, the first terms ar... | Mathematics | TestHub
- Let the sum of an infinite, whose first te... | Mathematics | TestHub
- Letandbe inand,andbe inIf the sum of first... | Mathematics | TestHub
- Letbe three real numbers such thatare in a... | Mathematics | TestHub
- For the two positive numbers, ifandare in... | Mathematics | TestHub
- There are four numbers of which the first... | Mathematics | TestHub
- If arithmetic mean of two distinct positiv... | Mathematics | TestHub
- Let the first three terms and , with , of... | Mathematics | TestHub
- Letand, terms of a non-constantbe respecti... | Mathematics | TestHub
- Let three real numbers be in arithmetic pr... | Mathematics | TestHub
- Letbe inandbe inThen, the arithmetic mean... | Mathematics | TestHub
- Let a_{n}=\frac{2^{3}-1}{2^{3}+1} \cdot \f... | Mathematics | TestHub
- Assume p, q and r are distinct positive in... | Mathematics | TestHub
- Distinct numbers a, b, c form an A.P., and... | Mathematics | TestHub
- Let a, b, c be in G.P. with ratio r , wher... | Mathematics | TestHub
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- Assume p, q and r are distinct positive in... | Mathematics | TestHub
- When 3^{37}=80 \lambda+k for an integer \l... | Mathematics | TestHub
- In a sequence of ( 4 n+1 ) terms, the firs... | Mathematics | TestHub
- Match each statement in Column I with all... | Mathematics | TestHub
- Sum of first n terms of a sequence is give... | Mathematics | TestHub
Special sequences/series(150)
- The sum of the series \sum_{n=1}^{\infty}... | Mathematics | TestHub
- Let S = \sum_{n=1}^{\infty} \frac{n^2+2n}{... | Mathematics | TestHub
- The sum of the infinite series S = \sum_{n... | Mathematics | TestHub
- Practice Question | Mathematics | TestHub
- The sum of the first terms of the series i... | Mathematics | TestHub
- If the sum of first terms of an is , then... | Mathematics | TestHub
- Let , denote the sum of the infinite geome... | Mathematics | TestHub
- The sum of the series is | Mathematics | TestHub
- The sum of the series upto terms is | Mathematics | TestHub
- Statement : The sum of the series is . Sta... | Mathematics | TestHub
- The sum of the series upto 15 terms is | Mathematics | TestHub
- If the sum of the series ... upto terms, w... | Mathematics | TestHub
- The sum . upto 11-terms is: | Mathematics | TestHub
- The sum of the series is | Mathematics | TestHub
- The sum of the series: . upto 10 terms, is: | Mathematics | TestHub
- Practice Question | Mathematics | TestHub
- Let. Then Sncan take value(s) | Mathematics | TestHub
- The sum of the series : upto 10 terms is : | Mathematics | TestHub
- If the sumup toterms is equal tothenis equ... | Mathematics | TestHub
- Let, wheredenotes the greatest integer les... | Mathematics | TestHub
- If , for all in , then is: | Mathematics | TestHub
- The sum of firstterms of the seriesis | Mathematics | TestHub
- The value ofis equal to: | Mathematics | TestHub
- The value ofis equal to | Mathematics | TestHub
- upto terms is | Mathematics | TestHub
- If the sum of the firstterms of the series... | Mathematics | TestHub
- Let. Ifthenis equal to: | Mathematics | TestHub
- Letforbe in A.P. such thatandIfis the leas... | Mathematics | TestHub
- Let and . Then, the least odd natural numb... | Mathematics | TestHub
- Let be the sum of the first terms and be t... | Mathematics | TestHub
- The sum of the firstterms of the seriesis | Mathematics | TestHub
- Letbe insuch thatandIfthenis equal to: | Mathematics | TestHub
- Ifwheredenotes theterm of a series, thenis | Mathematics | TestHub
- The sum of the following seriesup toterms,... | Mathematics | TestHub
- The sum of the seriesuptoterm is: | Mathematics | TestHub
- If the sum of the firstterms of the series... | Mathematics | TestHub
- Some identical balls are arranged in rows... | Mathematics | TestHub
- The sum,, is equal to | Mathematics | TestHub
- The sumis ___________. | Mathematics | TestHub
- If, then an ordered pairis equal to: | Mathematics | TestHub
- The sum of the infinite series is equal to | Mathematics | TestHub
- If the sum of the seriesup toterm isand th... | Mathematics | TestHub
- Letbe ansuch thatIf the sum of thisistheni... | Mathematics | TestHub
- is equal to | Mathematics | TestHub
- Letbe a sequence such thatandfor all. Then... | Mathematics | TestHub
- Ifare natural numbers such thatthen the sl... | Mathematics | TestHub
- If, thenis equal to _______. | Mathematics | TestHub
- The greatest integer less than or equal to... | Mathematics | TestHub
- Letbe an arithmetic progression withand co... | Mathematics | TestHub
- Let be a sequence such that and .Then is e... | Mathematics | TestHub
- If, whereandare co-prime, thenis equal to | Mathematics | TestHub
- Let forbe the sum of the infinite geometri... | Mathematics | TestHub
- If, then the maximum value ofis | Mathematics | TestHub
- Consider the sequencesuch thatandforIfthen... | Mathematics | TestHub
- The sumis equal to | Mathematics | TestHub
- Letandfor every natural number. Thenis equ... | Mathematics | TestHub
- Letand. Then, the value ofis equal to ____... | Mathematics | TestHub
- Letbe a sequence such thatandfor all. Then... | Mathematics | TestHub
- Let and . If and then is equal to | Mathematics | TestHub
- Ifthen the value ofis | Mathematics | TestHub
- The sum to terms of the series is equal to | Mathematics | TestHub
- Letdenote the greatest integer. Thenis equ... | Mathematics | TestHub
- The sumis _____ . | Mathematics | TestHub
- If and then is equal to | Mathematics | TestHub
- The sum to terms of the seriesis :- | Mathematics | TestHub
- The sum to infinite term of the series is | Mathematics | TestHub
- The sum of the seriesup toterms is | Mathematics | TestHub
- If , and , where , then equal to ______ | Mathematics | TestHub
- Letbe the sum to n-terms of an arithmetic... | Mathematics | TestHub
- The sum of the infinite series . is equal to: | Mathematics | TestHub
- The value of is | Mathematics | TestHub
- If upto , where and are integers with , th... | Mathematics | TestHub
- Let the first term of a series be and its... | Mathematics | TestHub
- If .to terms, then | Mathematics | TestHub
- If and , then the point lies on the line | Mathematics | TestHub
- If , then is equal to | Mathematics | TestHub
- If , then is equal to________ | Mathematics | TestHub
- If the set has elements and , where , then... | Mathematics | TestHub
- If where and are constants, then the value... | Mathematics | TestHub
- Letuptoterms and. If, thenis equal to ____... | Mathematics | TestHub
- then is equal to | Mathematics | TestHub
- The sum upto terms, is equal to | Mathematics | TestHub
- Let be a sequence such that and . Then is... | Mathematics | TestHub
- If , then is equal to : | Mathematics | TestHub
- For positive integers , if and , then the... | Mathematics | TestHub
- Let upto terms. If the sum of the first si... | Mathematics | TestHub
- If the sum of the first 10 terms of the se... | Mathematics | TestHub
- The sum . upto 20 terms, is equal to | Mathematics | TestHub
- If the sum of the first 20 terms of the se... | Mathematics | TestHub
- upto 40 terms is equal to | Mathematics | TestHub
- The value of is: | Mathematics | TestHub
- Let a_{n} denote the n-digit positive inte... | Mathematics | TestHub
- If \left(1^{2}-a\right)+\left(2^{2}-a_{2}\... | Mathematics | TestHub
- For n \geq 0 , define a_{n}=(\ln 10)^{n} \... | Mathematics | TestHub
- Find the sum \frac{3 \cdot 1^{3}}{1^{2}}+\... | Mathematics | TestHub
- Evaluate 1 / 2-1 /\left(2 \cdot 2^{2}\righ... | Mathematics | TestHub
- A positive sequence has each term from the... | Mathematics | TestHub
- Sum \frac{9}{5^{2} \cdot 2 \cdot 1}+\frac{... | Mathematics | TestHub
- If a_{k}=\frac{1}{k(k+1)} , for k=1,2,3 \l... | Mathematics | TestHub
- If the m th term of t_{n}=\sqrt{n} /(n+200... | Mathematics | TestHub
- Find the \mathrm{n}^{\text {th }} term and... | Mathematics | TestHub
- Evaluate 1 / 2-1 /\left(2 \cdot 2^{2}\righ... | Mathematics | TestHub
- Let a_{1} be the maximum of f(x)=1 /(2+\lf... | Mathematics | TestHub
- Let S=\sum_{n=1}^{99} \frac{5^{100}}{(25)^... | Mathematics | TestHub
- A sequence is obtained by deleting all per... | Mathematics | TestHub
- Let d_{1}, \ldots, d_{k} be all positive d... | Mathematics | TestHub
- Find 1 / 9+1 / 18+1 / 30+1 / 45+1 / 63+\cd... | Mathematics | TestHub
- Define T_{r}=(1+2+\cdots+r)^{2} /(1+3+\cdo... | Mathematics | TestHub
- If the sum of the n terms of the series 1^... | Mathematics | TestHub
- Given \sum_{n=1}^{\infty} 1 / n^{2}=\pi^{2... | Mathematics | TestHub
- Find 1 /(3 \times 7)+1 /(7 \times 11)+1 /(... | Mathematics | TestHub
- For n \geq 0 , define a_{n}=(\ln 10)^{n} \... | Mathematics | TestHub
- If x^{6}=2 x^{3}-1 and x is nonreal, evalu... | Mathematics | TestHub
- Let x_{1}=1 / 2 and x_{k+1}=x_{k}^{2}+x_{k... | Mathematics | TestHub
- Let S_{k}=\frac{1+2+\cdots+k}{k} and \sum_... | Mathematics | TestHub
- The numbers of positive divisors of 6912,... | Mathematics | TestHub
- Find 1+9 / 4+36 / 9+100 / 16+\cdots throug... | Mathematics | TestHub
- Find the twentieth term of 2,9,20,35,54, \... | Mathematics | TestHub
- Let x_{1}=1 / 2 and x_{k+1}=x_{k}^{2}+x_{k... | Mathematics | TestHub
- A positive sequence has each term from the... | Mathematics | TestHub
- Find the twentieth term of 2,9,20,35,54, \... | Mathematics | TestHub
- Let \left\{a_{n}\right\} satisfy a_{1}+\cd... | Mathematics | TestHub
- Sum of n terms of series a b+(a+1)(b+1)+(a... | Mathematics | TestHub
- Let a_{1}=2 and a_{n}-a_{n-1}=n^{2} for n... | Mathematics | TestHub
- If S_{n}=1 . n+2 .(n-1)+3 .(n-2)+\ldots \l... | Mathematics | TestHub
- Evaluate \sum_{r=1}^{10} \frac{(1+2+\cdots... | Mathematics | TestHub
- For n a positive integer, set \mathrm{S}(\... | Mathematics | TestHub
- For positive x>y , define a_{n}=x^{1 / 2^{... | Mathematics | TestHub
- Let \mathrm{S}=\sqrt{1+\frac{1}{1^{2}}+\fr... | Mathematics | TestHub
- For every positive integer n, Σ(r=1 to n)... | Mathematics | TestHub
- Use \sum_{k=1}^{n} k=\frac{n(n+1)}{2}, \su... | Mathematics | TestHub
- Let a_{1} be the maximum of f(x)=1 /(2+\lf... | Mathematics | TestHub
- If (1+3+\cdots+a)+(1+3+\cdots+b)=1+3+\cdot... | Mathematics | TestHub
- Let S_{r}=2+4+6+\ldots ( r terms). Then | Mathematics | TestHub
- If 1^{2}+2 \cdot 2^{2}+3^{2}+2 \cdot 4^{2}... | Mathematics | TestHub
- Let S_{k}=1+1 / 2+\cdots+1 / k for positiv... | Mathematics | TestHub
- Find the sum of the infinite series \frac{... | Mathematics | TestHub
- For positive x>y , define a_{n}=x^{1 / 2^{... | Mathematics | TestHub
- Evaluate the first n terms of \frac{1}{1!}... | Mathematics | TestHub
- 2+4+7+11+16+\ldots to n terms = | Mathematics | TestHub
- The arithmetic mean of 9,99,999, \ldots, 9... | Mathematics | TestHub
- Let A=\sum_{i=1}^{10} \sum_{j=1}^{10} \min... | Mathematics | TestHub
- For positive integer r let T_{r}=1 /[\math... | Mathematics | TestHub
- If x^{6}=2 x^{3}-1 and x is nonreal, evalu... | Mathematics | TestHub
- Evaluate \sum_{k=1}^{n}\left(k^{2}+1\right... | Mathematics | TestHub
- Evaluate the first n terms of \frac{1}{1!}... | Mathematics | TestHub
- Let \left\{\mathrm{a}_{\mathrm{n}}\right\}... | Mathematics | TestHub
- The sum of the series \frac{x}{1-x^{2}}+\f... | Mathematics | TestHub
- Given \sum_{n=1}^{\infty} 1 / n^{2}=\pi^{2... | Mathematics | TestHub
- If S_{n}=\sum_{r=1}^{n}t_{r}=\frac{1}{6}n\... | Mathematics | TestHub
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