Sequence And Series Question 281
Question: If $ a^{x}=b^{y}=c^{z},anda,b,c $ are in G.P. then $ x,y,z $ are in
[Pb. CET 1993; DCE 1999; AMU 1999]
Options:
A) A. P.
B) G. P.
C) H. P.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \because a,b,c $ are in G.P.
Þ $ b^{2}=ac $ ?..(i) Let $ a^{x}=b^{y}=c^{z}=k $
Þ $ a={k^{1/x}},b={k^{1/y}},c={k^{1/z}} $ Putting these values in (i), $ {k^{2/y}}={k^{1/x}}.{k^{1/z}} $ $ ={k^{\frac{1}{x}+\frac{1}{z}}} $ i.e., $ \frac{2}{y}=\frac{1}{x}+\frac{1}{z} $
$ \therefore \frac{1}{x},\frac{1}{y},\frac{1}{z} $ are in A.P. or $ x,y,z $ are in H.P.
BETA
