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Question
Show that the products of the corresponding terms of the sequences a, ar, ar2, …arn – 1 and A, AR, AR2, … `AR^(n-1)` form a G.P, and find the common ratio
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Solution
% Sequence a, ar, ar2, …. The sequence formed by the product of arn – 1 and the corresponding terms of A, AR, AR2, .... ARn – 1
`("Second term")/("First term")` = `(arAR)/(aA) = rR`
`("Third term")/("Second term")` = `(ar^2 AR^2)/(arAR) = rR`
Thus, the above sequence forms a G.P. and the common ratio is rR.
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