Q. 525.0( 3 Votes )

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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.

Answer :

Ist G.P :a, ar, ar

^{2}, …….ar

^{n – 1}

2^{nd} G.P. : A, AR, AR^{2},….. AR^{n – 1 }

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

(aA), (aA),(rR), (aR)r^{2}R^{2},…..(aA)r^{n – 1} R^{n – 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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