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Question
In a G.P. of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the G.P. is ______.
Options
`(-4)/5`
`1/5`
4
None the these
Solution
In a G.P. of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the G.P. is 4.
Explanation:
Let us consider a G.P. a, ar, ar2, ... with 2n terms.
We have `(a(r^(2n) - 1))/(r - 1) = (5a((r^2)^n - 1))/(r^2 - 1)`
Since common ratio of odd terms will be r2 and number of terms will be n
⇒ `(a(r^(2n) - 1))/(r - 1) = 5 (a(r^(2n) - 1))/((r^2 - 1))`
⇒ a(r + 1) = 5a
i.e., r = 4
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