Sequence And Series Question 247
Question: If $ a,\ b,\ c $ are in H.P., then $ \frac{a}{b+c},\ \frac{b}{c+a},\ \frac{c}{a+b} $ are in
[Roorkee 1980]
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
If $ a,\ b,\ c $ are in H.P. $ \frac{1}{a}+\frac{1}{c}=\frac{2}{b} $ are also in A.P.
$ \Rightarrow $ $ \frac{a+b+c}{a},\ \frac{a+b+c}{b},\ \frac{a+b+c}{c} $ are in A.P.
$ \Rightarrow $ $ \frac{b+c}{a},\ \frac{a+c}{b},\ \frac{a+b}{c} $ are in A.P.
$ \Rightarrow $ $ \frac{a}{b+c},\ \frac{b}{a+c},\ \frac{c}{a+b} $ are in H.P.
BETA
