Question

A GP consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, the common ratio will be equal to ______.

पर्याय

• 2

• 3

• 4

• 5

Answer 1

A GP consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, the common ratio will be equal to 4.

Explanation:

Let G.P. is a, ar, ar², ...... ar^2n–1

Sum = `(a(1 - r^(2n)))/(1 - r)` = S₁  ....(1)

Terms occupying odd places are a, ar², ar⁴ ......

Sum = `(a(1 - r^(2n)))/(1 - r)` = S₂  ....(2)

Given S₁ = 5S₂

`(a(1 - r^(2n)))/(1 - r) = (5a(1 - r^(2n)))/(1 - r^2)`

⇒ 1 + r = 5

⇒ r = 4