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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, y` and `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
Given x, 2y and 3z are in AP ,
then ,`2y=(x+3z)/(2)`
`implies y=(x+3z)/(4)`
`implies 4y=x+3z`
and x,y,z are in GP
then `(y)/(x)=(z)/(y) =lamda`
`implies y=x lamda and z=lamday - lamda^(2)x`
On subsitiuting these values in Eq (i) we get
`4(x, lamda )=x+3(lamda^(2)x)`
`implies 4lamdax=x+3lamda^(2)x`
`implies 4lamda=1+3lamda^(2)`
`implies 3lamda ^(2) -4lamda+1=0`
`=(3lamda-10(lamda-1)=0`
`therefore lamda =(1)/(3).lamda =1 `
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