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If the pth ,qth and rth terms of an AP a...

If the pth ,qth and rth terms of an AP are in G.P then the common ration of the GP is

A

`pr/q^2`

B

`r/p`

C

`(q+r)/(p+q)`

D

`(q-r)/(p-q)`

Text Solution

Verified by Experts

The correct Answer is:
D
pth,qth,rth terms of A.P. are
a+(p-1)d=x (1)
a+(q-1)d=xR (2)
`a+(r-1)d=xR^(2)` (3)
where R is common ratio of G.P.
Subtracting (2) from (3) and (1) from (2) and then dividing the former by the later, we have
`(q-r)/(p-q)=(xR^(2)-xR)/(xR-x)=R`
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