Sequence And Series Question 283
Question: If $ \log (x+z)+\log (x+z-2y)=2\log (x-z),, $ then $ x,,y,,z $ are in
[RPET 1999]
Options:
A) H.P.
B) G.P.
C) A.P.
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \log ,(x+z)+\log (x+z-2y)=2\log (x-z) $ $ \log (x+z)(x+z-2y)=\log {{(x-z)}^{2}} $ $ xz-xy-yz=-xz $
$ \Rightarrow 2xz=xy+yz $ Dividing by $ x,y,z, $ we get
Þ $ \frac{2}{y}=\frac{1}{x}+\frac{1}{z} $ i.e., $ \frac{1}{x},\frac{1}{y},\frac{1}{z} $ are in A.P.
Þ $ x,y,z $ are in H.P.
BETA
