Show that the products of the corresponding terms of the sequences $a, a r, a r^{2}, . . . . a r^{n - 1}$ and $A, A R, A R^{2}, . . . . A R^{n - 1}$ form a G.P and findthe common ratio.

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Solution

Product of corresponding terms is $\Rightarrow (a) (A), (a r) (A R), (a r^{2}) (A R^{2}) . . . . . (a r^{m - 1}) (A R^{x - 1})$
$= a A, a A r R, a A (r R)^{2}, . . . . . . a A (r R)^{x - 1}$
Clearly, this is a $G P$ and the common ratio is $(r R)$

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Show that the products of the corresponding terms of the sequences a,ar,ar2,....arn−1 and A,AR,AR2,....ARn−1 form a G.P and findthe common ratio.

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Show that the products of the corresponding terms of the sequences $a, a r, a r^{2}, . . . . a r^{n - 1}$ and $A, A R, A R^{2}, . . . . A R^{n - 1}$ form a G.P and findthe common ratio.

Product of corresponding terms is $\Rightarrow (a) (A), (a r) (A R), (a r^{2}) (A R^{2}) . . . . . (a r^{m - 1}) (A R^{x - 1})$
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