Sequence And Series Question 197
Question: If $ {a^{1/x}}={b^{1/y}}={c^{1/z}} $ and $ a,\ b,\ c $ are in G.P., then $ x,\ y,\ z $ will be in
[IIT 1969; UPSEAT 2001]
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ {a^{1/x}}={b^{1/y}}={c^{1/z}}=k\Rightarrow a=k^{x},,b=k^{y},\ c=k^{z} $ Now, $ a,\ b,\ c $ are in G.P.
$ \Rightarrow $ $ b^{2}=ac\Rightarrow k^{2y}=k^{x}.k^{z}={k^{x+z}}\Rightarrow 2y=x+z $
$ \Rightarrow $ $ x,\ y,\ z $ are in A.P.
BETA
