Sequence And Series Question 252
Question: If $ \frac{a+b}{1-ab},\ b,\ \frac{b+c}{1-bc} $ are in A.P., then $ a,\ \frac{1}{b},\ c $ are in
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{a+b}{1-ab},\ b,\ \frac{b+c}{1-bc} $ are in A.P.
$ \Rightarrow $ $ b-\frac{a+b}{1-ab}=\frac{b+c}{1-bc}-b $
$ \Rightarrow $ $ -\frac{a(b^{2}+1)}{1-ab}=\frac{c(b^{2}+1)}{1-bc} $
$ \Rightarrow $ $ -( \frac{1-ab}{a} )=\frac{1-bc}{c} $
$ \Rightarrow $ $ -\frac{1}{a}+b=\frac{1}{c}-b $
$ \Rightarrow $ $ 2b=\frac{1}{a}+\frac{1}{c} $
$ \Rightarrow $ $ a,\ \frac{1}{b},\ c $ are in H.P.
BETA
