Sequence And Series Question 284
Question: If $ \frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b} $ are in H.P., then $ a,b,c $ are in
[RPET 1999]
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b} $ are in H.P. Its reciprocal is, $ \frac{b+c}{a},\frac{c+a}{b},\frac{a+b}{c} $ are in A.P. Add 1 to each term, we get $ \frac{a+b+c}{a},\frac{a+b+c}{b},\frac{a+b+c}{c} $
$ \Rightarrow \frac{1}{a},\frac{1}{b},\frac{1}{c} $ are in A.P.
Þ $ a,,b,,c $ are in H.P.
BETA
