Sequence And Series Question 263
Question: If $ \frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx}(x\ne 0) $ , then $ a,\ b,\ c,\ d $ are in
[RPET 1986]
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx} $ Applying componendo and dividendo, we get $ \frac{2a}{2bx}=\frac{2b}{2cx}=\frac{2c}{2dx} $
$ \Rightarrow $ $ b^{2}=ac $ and $ c^{2}=bd $
$ \Rightarrow $ $ a,\ b,\ c $ and $ b,\ c,\ d $ are in G.P. Therefore, $ a,\ b,\ c,\ d $ are in G.P.
BETA
