Show that the products of the corresponding terms of the sequences a, ar, ar²,…ar^{n – 1} and A, AR, AR², … AR^{n – 1} form a G.P, and find the common ratio.

Question

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.

Philoid · Accepted Answer

Given: The sequences a, ar, ar²,…ar^{n – 1} and A, AR, AR², … AR^{n – 1}

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

a × A, ar × AR, ar² × AR², ……….., arⁿ × ARⁿ

Here,

= rR

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

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.

Show that the products of the corresponding terms of the sequences a, ar, ar²,…ar^{n – 1} and A, AR, AR², … AR^{n – 1} form a G.P, and find the common ratio.