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The pth, (2p)th and (4p)th terms of an A...

The pth, `(2p)th` and `(4p)th` terms of an AP, are in GP, then find the common ratio of GP.

Text Solution

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Let `T_(n)=An+B`
` :. T_(p)=Ap+B,`
`T_(2p)=2Ap+B,T_(4p)=4Ap+B`
`:.T_(p),T_(2p)T_(4p)` are in GP.
`:.(2Ap+B)^(2)=(Ap+B)(4Ap+B)`
`implies ABp=0`
`:.B=0,A ne 0,p ne 0`
` implies` Common ratio, `r=(T_(2p))/(T_(p))=(2Ap+0)(Ap+0)=2`.
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