# 20.  Show that the products of the corresponding terms of the sequences    $a,ar, ar^2 , ...ar^{n-1} \: \: and\: \: A ,AR, AR^2 ....AR^{n-1}$ form a G.P, and find the common ratio.

S seema garhwal

To prove : $aA,arAR,ar^2AR^2,...................$     is a GP.

$\frac{second \, \, term}{first\, \, term}=\frac{arAR}{aA}=rR$

$\frac{third \, \, term}{second\, \, term}=\frac{ar^2AR^2}{arAR}=rR$

Thus, the above sequence is a GP with common ratio of rR.

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