Mathematics - Sequence & Series Question with Solution | TestHub
Match each item in List I to all applicable entries in List II.
List I | List II |
|---|---|
(A) Two positive numbers have arithmetic mean 6; their geometric mean G and harmonic mean H satisfy G²+3H=48. Find their product. | (P) 2/7 |
(B) Find Σ(k=0 to infinity) (6k+5)/[(3k+1)²(3k+4)²]. | (Q) 32 |
(C) The first two terms of an H.P. are 1/2,1/3. Find the harmonic mean of its first four terms. | (R) 1/3 |
(D) Find the principal, nonnegative geometric mean of -4 and -9. | (S) 6 |
| (T) -6 |
Options:
Answer:
Solution:
(A) The sum is 12 and H=ab/6, while G²=ab. Thus ab+3ab/6=48 gives ab=32. (B) Each summand equals (1/3)[1/(3k+1)²-1/(3k+4)²]; the series telescopes to 1/3. (C) The first four H.P. terms are 1/2,1/3,1/4,1/5, whose harmonic mean is 4/(2+3+4+5)=2/7. (D) The requested principal nonnegative mean is √[(-4)(-9)]=6. Thus A-Q; B-R; C-P; D-S.
