Sequence And Series Question 300
Question: If a,b,c are in A.P., then $ {2^{ax+1}},{2^{bx+1}},,{2^{cx+1}},x\ne 0 $ are in
[DCE 2000; Pb. CET 2000]
Options:
A) A.P.
B) G.P. only when $ x>0 $
C) G.P. if $ x<0 $
D) G.P. for all $ x\ne 0 $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{T_2}{T_1}=\frac{T_3}{T_2} $
$ \Rightarrow {2^{(b-a)x}}={2^{(c-b)x}} $
$ \Rightarrow (b-a)x=(c-b)x $
Þ $ (b-a)=(c-b) $ $ \forall ,x,x\ne 0 $
$ \therefore {2^{ax+1}},{2^{bx+1}},{2^{cx+1}} $ is a G.P., $ \forall x\ne 0. $
BETA
