# 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 find the common ratio.

Ist G.P :a, ar, ar2, …….arn – 1

2nd G.P. : A, AR, AR2,….. ARn – 1

The sequence formed after multiplying the corresponding terms of the sequences is

(aA), (aA),(rR), (aR)r2R2,…..(aA)rn – 1 Rn – 1

Here = = rR

= = rR

= = rR

Since the ratios of two succeeding terms are the same, the resulting sequence is also a G.P.

The common ratio of the new G.P. = (rR).

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