Sequence And Series Question 202
Question: If $ b^{2},,a^{2},,c^{2} $ are in A.P., then $ a+b,,b+c,,c+a $ will be in
[AMU 1974]
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Given that $ b^{2},\ a^{2},\ c^{2} $ are in A.P. Therefore $ a^{2}-b^{2}=c^{2}-a^{2} $
$ \Rightarrow $ $ (a-b)(a+b)=(c-a)(c+a) $
$ \Rightarrow $ $ \frac{a-b}{c+a}=\frac{c-a}{a+b} $
$ \Rightarrow $ $ \frac{b-a+c-c}{(c+a)(b+c)}=\frac{a+b-b-c}{(b+c)(a+b)} $
$ \Rightarrow $ $ \frac{1}{b+c}-\frac{1}{a+b}=\frac{1}{c+a}-\frac{1}{b+c} $
$ \Rightarrow $ $ \frac{1}{a+b},\ \frac{1}{b+c},\ \frac{1}{c+a} $ are in A.P. Hence $ (a+b),\ (b+c),\ (c+a) $ are in H.P.
BETA
