Sequence And Series Question 322
Question: If $ a^{2},,b^{2},,c^{2} $ be in A.P., then $ \frac{a}{b+c},,\frac{b}{c+a},,\frac{c}{a+b} $ will be in
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Since $ a^{2},\ b^{2},\ c^{2} $ be in A.P. Then $ b^{2}-a^{2}=c^{2}-b^{2} $
$ \Rightarrow $ $ (b-a)(b+a)=(c-b)(c+b) $
Þ $ \frac{b-a}{c+b}=\frac{c-b}{b+a} $
Þ $ \frac{(b-a)(a+b+c)}{(c+a)(b+c)}=\frac{(c-b)(a+b+c)}{(a+b)(c+a)} $
$ \Rightarrow $ $ \frac{b^{2}+bc-ac-a^{2}}{(c+a)(b+c)}=\frac{c^{2}+ac-ab-b^{2}}{(a+b)(c+a)} $
$ \Rightarrow $ $ \frac{b}{c+a}-\frac{a}{b+c}=\frac{c}{a+b}-\frac{b}{c+a} $ Hence $ \frac{a}{b+c},\ \frac{b}{c+a},\ \frac{c}{a+b} $ be in A.P.
BETA
