Sequence And Series Question 88
Question: If x, 2y, 3z are in A.P. where the distinct numbers x, y, z are in G.P., then the common ratio of the G.P. is
Options:
A) 3
B) $ \frac{1}{3} $
C) 2
D) $ \frac{1}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] x, y, and z are in G.P. Hene, $ y=xr,z=xr^{2} $ Also, x, 2y, and 3z are in A.P. Hence, $ 4y=x+3z $
$ \Rightarrow 4xr=x+3xr^{2} $
$ \Rightarrow 3r^{2}-4r+1=0 $
$ \Rightarrow (3r-1)(r-1)=0 $
$ \Rightarrow r=1/3 $ ( $ r\ne 1 $ is not possible as x, y, z are distinct)
BETA
