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Question

A. G.P. consists of of an even numbers of terms . If the sum of all the terms is 5 times the sum of terms occupying odd places, the find its common ratio.

Solution
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Let the G.P. be T1,T2,T3,T4,...T2n
Number of terms =2n
According to the given condition,
T1+T2+T3+...+T2n=5[T1+T3+...+T2n1]T1+T2+T3+...+T2n5[T1+T3+...+T2n1]=0T2+T4+...+T2n=4[T1+T3+...+T2n1]
Let the G.P. be a,ar,ar2,ar3,...
ar2((r2)n1)r21=4×a((r2)n1)r21ar2=4ar=±2
Thus the common ratio of the G.P. is ±2.

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