Sequence And Series Question 208
Question: If $ a^{2},\ b^{2},\ c^{2} $ are in A.P., then $ {{(b+c)}^{-1}},\ {{(c+a)}^{-1}} $ and $ {{(a+b)}^{-1}} $ will be in
[Roorkee 1968; RPET 1996]
Options:
A) H.P.
B) G.P.
C) A.P.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ a^{2},\ b^{2},\ c^{2} $ are in A.P. Therefore $ a^{2}+(ab+bc+ca) $ , $ b^{2}+(ab+bc+ca) $ , $ c^{2}+(ab+bc+ca) $ will be in A.P.
$ \Rightarrow $ $ {a(a+b)+c,(a+b)},\ {b(b+a)+c,(b+a)},\ $ $ c(c+b)+a(b+c) $ will be in A.P.
Þ $ (a+b)(a+c),\ (b+a)(b+c),\ (c+a)(c+b) $ will be in A.P.
$ \Rightarrow $ $ \frac{1}{b+c},\ \frac{1}{c+a},\ \frac{1}{a+b} $ will be in A.P.{Dividing each term by $ f(n+3)+3f(n+1)=f(n)+3f(n+2) $ }
BETA
