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

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Solution

Multiplying the corresponding terms of the given sequences, we have :

$(a \times A), (a r \times A R), (a r^{2} \times A R^{2}), . . . . (a r^{n - 1} \times A R^{n - 1})$

i.e. $(a A), (a A r R), (a A r^{2} R^{2}) . . . . (a A r^{n - 1} R^{n - 1})$

Which is a G.P. having common ratio = $\frac{a A r R}{a A} = r R$

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