If the 10 t h , term of an A.P. is 1 20 , and its 20 t h , term is 1 10 , then the sum of its first 200 , terms is.

Let, a & d is the first term and common difference of arithmetic progression respectively, then T 10 = 1 20 = a + 9 d . . . i T 20 = 1 10 = a + 19 d . . . i i After solving i and i i , we get a = 1 200 , d = 1 200 Now S 200 = 200 2 2 200 + 199 200 = 201 2 = 100 1 2 .

Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesA.P.Easy2 minPYQ_2020

MathematicsEasystatement

If the $10^{t h}$ , term of an A.P. is $\frac{1}{20}$ , and its $20^{t h}$ , term is $\frac{1}{10}$ , then the sum of its first $200$ , terms is.

Options:

Answer:

Solution:

Let, $a & d$ is the first term and common difference of arithmetic progression respectively, then

$T_{10} = \frac{1}{20} = a + 9 d . . . (i)$
$T_{20} = \frac{1}{10} = a + 19 d . . . (i i)$

After solving $(i)$ and $(i i)$ , we get
$a = \frac{1}{200}, d = \frac{1}{200}$

Now

$S_{200} = \frac{200}{2} [\frac{2}{200} + \frac{199}{200}] = \frac{201}{2} = 100 \frac{1}{2}$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:A.P.

⏱ 2mℹ️ Source: PYQ_2020

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