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if x , 2y and 3z are in AP where the d...

if x , 2y and 3z are in AP where the distinct numbers x, yand z are in gp. Then the common ratio of the GP is

A

3

B

`1/3`

C

2

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
B
x,y and z are in G.P. Hence,
`y=xr,=xr^(2)`
Also,x,2y, and 3z are in A.P. Hnce,
4y=x+3z
`rArr4xr=x+3xr^(2)`
`rArr3r^(2)-4r+1=0`
`rArr(3r-1)(r-1)=0`
`rArrr=1//3` (rne1 is not possible as x,y,z are distinct)
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