Sequence And Series Question 324
Question: If p,q,r are in G.P and $ {{\tan }^{-1}}p $ , $ {{\tan }^{-1}}q,{{\tan }^{-1}}r $ are in A.P. then p, q, r are satisfies the relation
[DCE 2005]
Options:
A) $ p=q=r $
B) $ p\ne q\ne r $
C) $ p+q=r $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ p,q,r\in G\text{.},P\text{.} $ ,
$ \therefore q^{2}=pr $ Also $ {{\tan }^{-1}}p,{{\tan }^{-1}}q, $ $ {{\tan }^{-1}}r\in $ A.P.
Þ $ {{\tan }^{-1}}p+{{\tan }^{-1}}r=2{{\tan }^{-1}}q $
Þ $ p+r=2q\Rightarrow p,q,r $ are in A.P. Now p, q, r are both in A.P and G.P., which is possible only, if $ p=q=r $ .
BETA
