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

Answer

N/a

Explanation

Let G.P. be `a, ar, ar^(2), ar^(3), ar^(4), ar^(5), …` and be the number of terms.
Given that,
Sum of (2n) terms of progression
= 5 (sum of terms at odd positions of progression)
`rArr` Sum of 2n terms of `a + ar + ar^(2) + ...`
= 5 (sum of n terms `a + ar^(2) + ar^(4) + …`)
`rArr` `(a(1 - r^(2n)))/(1 - r) = 5 * (a{1 - (r^(2))^(n)})/(1 - r^(2))`
`rArr` `(a(1 - r^(2n)))/(1 - r) = 5 * (a(1 - r^(2n)))/((1 - r)(1 + r))`
`rArr` 1 + r = 5 `" " rArr" "` r = 4.