Sequence And Series Question 214
Question: If $ a,\ b,\ c $ are in A.P. and $ |a|,\ |b|,\ |c|\ <1 $ and $ x=1+a+a^{2}+……..\infty $ $ y=1+b+b^{2}+…….\infty $ $ z=1+c+c^{2}……..\infty $ Then $ x,\ y,\ z $ shall be in
[Karnataka CET 1995; AIEEE 2005]
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Clearly $ x=\frac{1}{1-a},\ y=\frac{1}{1-b},\ z=\frac{1}{1-c} $ Since $ a,\ b,\ c $ are in A.P.
$ \Rightarrow $ $ 1-a,\ 1-b,\ 1-c $ are also in A.P.
$ \Rightarrow $ $ \frac{1}{1-a},\ \frac{1}{1-b},\ \frac{1}{1-c} $ are in H.P.
$ \therefore $ $ x,\ y,\ z $ are in H.P.
BETA
