Sequence And Series Question 269
Question: If $ x^{a}={x^{b/2}}{z^{b/2}}=z^{c} $ , then $ a,b,c $ are in
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ x^{a}={x^{b/2}}{z^{b/2}}=z^{c}=\lambda $
$ \Rightarrow $ $ x={{\lambda }^{1/a}},\ z={{\lambda }^{1/c}},\ xz={{\lambda }^{2/b}} $
$ \Rightarrow $ $ {{\lambda }^{(1/a)+(1/c)}}={{\lambda }^{2/b}} $
$ \Rightarrow $ $ \frac{1}{a}+\frac{1}{c}=\frac{2}{b} $
$ \Rightarrow $ $ a,\ b,\ c $ are in H.P.
BETA
