Q. 204.4( 58 Votes )

# 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 :

Given: The sequences a, ar, ar^{2},…ar^{n – 1} and A, AR, AR^{2}, … AR^{n – 1}

The products of the corresponding terms of the G.P is

a × A, ar × AR, ar^{2} × AR^{2}, ……….., ar^{n} × AR^{n}

Here,

= rR

= rR

∴ The product of the corresponding terms of the given sequence forms a G.P and the common ratio is rR

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