A. G.P. consists of an even number of terms. If the sum of all theterm – InterviewSolution

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1.	A. G.P. consists of an even number of terms. If the sum of all theterms is 5 times the sum of the terms occupying he odd places. Find thecommon ratio of the G.P.
Answer» Correct Answer - `r=4` Let us consider a GP with first term a and common ratio r and having 2n terms. Then, `T_(1)+T_(2)+T_(3)+T_(4)+...+T_(2n)=5(T_(1)+T_(3)+T_(5)+...+T_(2n-1))` `rArr a+ar+ar^(2)+...+ar^((2n-1))=5[a+ar^(2)+ar^(4)+...+ar^((2n-2))]` `rArr a((1-r^(2n))/(1-r))=5a [(1-(r^(2))^(n))/(1-r^(2))] rArr 1+r=5 rArr r=4`.

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