Sequence And Series Question 450
Question: If $ x>1,\ y>1,z>1 $ are in G.P., then $ \frac{1}{1+In,x},\ \frac{1}{1+In,y}, $ $ \ \frac{1}{1+In,z} $ are in
[IIT 1998; UPSEAT 2001]
Options:
A) A.P.
B) H.P.
C) G.P.
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ x,\ y,\ z $ are in G.P. Hence $ y^{2}=xz $
$ \therefore $ $ 2\log y=\log x+\log z $
$ \Rightarrow $ $ 2(\log y+1)=(1+\log x)+(1+\log z) $
$ \Rightarrow $ $ 1+\log x,\ 1+\log y,\ 1+\log z $ are in A.P.
$ \Rightarrow $ $ \frac{1}{1+\log x},\ \frac{1}{1+\log y},\ \frac{1}{1+\log z} $ are is H.P.
BETA
