# A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying the odd places.

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A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying the odd places. Find the common ratio of the G.P.

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Let there be n terms.

a, ar, ar2, ar3, ……………..arn - 2, arn - 1

The sum of a G.P. = $\frac{a(r^n-1)}{r-1}$

Odd terms of the sequence are:

a, ar2, ar4……………..arn - 2

⇒ r + 1 = 5

⇒ r = 4.