Show that the products of the corresponding terms of the sequences form a G.P, and find the common ratio.

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Solution

Given that the sequence a, ar, a r 2 ........a r n−1 and A, AR, A R 2 ,.............A R n−1 .

Now, the product of both the series by its corresponding term is,

a( A ), ar( AR ), a r 2 ( A R 2 )........a r n−1 ( A R n−1 )

Now,

Second term First term = arAR aA =rR

Third term Second term = a r 2 A R 2 arAR =rR

Thus, the product of both the series by its corresponding term in the forms of G.P and the common ratio is rR.

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