Sequence And Series Question 321
Question: When $ \frac{1}{a}+\frac{1}{c}+\frac{1}{a-b}+\frac{1}{c-d}=0 $ and $ b\ne a\ne c $ , then $ a,\ b,\ c $ are
[MP PET 2004]
Options:
A) In H.P.
B) In G.P.
C) In A.P.
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ \frac{1}{a}+\frac{1}{c}+\frac{1}{a-b}+\frac{1}{c-b}=0 $ $ \frac{1}{a}+\frac{1}{c-b}=\frac{1}{b-a}-\frac{1}{c} $
$ \Rightarrow $ $ \frac{c-b+a}{a(c-b)}=\frac{c-b+a}{(b-a)c} $
$ \Rightarrow $ $ ac-ab=bc-ac $
$ \Rightarrow $ $ 2ac=ab+bc $
$ \Rightarrow $ $ \frac{2ac}{a+c}=b $ i.e., $ a,b,c $ are in H.P.
BETA
