Mathematics - Sequence & Series Question with Solution | TestHub
Match each statement in Column I with all valid progression types in Column II.
Column I | Column II |
|---|---|
(A) If the pth, qth and rth terms of a G.P. (common ratio ≠ 1) are in G.P., classify p, q, r. | (P) Arithmetic progression |
(B) Nonzero reals a, b, c, d satisfy (a²+b²+c²)(b²+c²+d²)<(ab+bc+cd)² and c(a-b)=a(b-c); classify a, b, c, d. | (Q) Geometric progression |
(C) Four distinct positive a, b, c, d are in G.P.; classify (a/b)(2 log a+log b), (b/c)(2 log b+log c), (c/d)(2 log c+log d). | (R) Harmonic progression |
(D) a₁,a₂,a₃ are in A.P., a₂,a₃,a₄ in G.P., and a₃,a₄,a₅ in H.P.; classify a₁,a₃,a₅. | (S) Not a harmonic progression (T) All terms identical |
Options:
Answer:
Solution:
(A) The G.P. condition gives , so are in A.P.; with distinct ratio they are not in H.P. (B) The conditions force equality, so all terms are identical and hence are simultaneously A.P., G.P. and H.P. (C) Direct substitution gives an A.P., and it is not H.P. (D) Eliminating from , and gives , so are in G.P. and not H.P.
