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If x ,2y ,3z are in A.P., where the dist...

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 a.`3` b. `1/3` c. `2` d. `1/2`

A

3

B

`1/3`

C

2

D

`1/2`

Text Solution

Verified by Experts

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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