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  4. If pth, qth, rth terms of a G.P. are in G.P., then p, q, r are in

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Q. If pth, qth, rth terms of a G.P. are in G.P., then p, q, r are in

Sequences and Series

Solution:

Since $T_{p}, T_{q}, T_{r} $ are in $G.P$.
$\therefore T_{q}^{2} = T_{p}.T_{r} $
$ \therefore \left(AR^{q-1}\right)^{2} = AR^{p-1}.AR^{r-1} $
$ \Rightarrow 2q-2 = p+r-2 $
$\Rightarrow 2q=p+r $
$ \Rightarrow p,q,r$ are in $A.P$.