Sequence And Series Question 497

Question: If $ a,\ b,\ c $ are in H.P., then which one of the following is true

[MNR 1985]

Options:

A) $ \frac{1}{b-a}+\frac{1}{b-c}=\frac{1}{b} $

B) $ \frac{ac}{a+c}=b $

C) $ \frac{b+a}{b-a}+\frac{b+c}{b-c}=1 $

D) None of these

Show Answer

Answer:

Correct Answer: D

Solution:

$ a,\ b,\ c $ are in H.P.
$ \Rightarrow $ $ b=\frac{2ac}{a+c} $ By inspection, we get (a) False (b) False (c) False