Question

The sum of infinite number of terms of a decreasing G.P. is 4 and the sum of the terms to m squares of its terms to infinity is `16/3`, then the G.P. is ______.

Options

• `2, 1, 1/2, 1/4, ....`

• `1/2, 1/4, 1/8,......`

• 2, 4, 8, ....

• `1/4, 1/8, 1/16 .......`

Answer 1

The sum of infinite number of terms of a decreasing G.P. is 4 and the sum of the terms to m squares of its terms to infinity is `16/3`, then the G.P. is `underlinebb(2, 1, 1/2, 1/4, ....)`.

Explanation:

Let G.P. is a, ar, ar² ...........

Sum of its terms = `a/(1 - r)` = 4 ...(1)

Sum of square of its terms = `a^2/(1 - r^2) = 16/3`  ...(2)

From (1) and (2)

`(16(1 - r)^2)/(1 - r^2) = 16/3`

⇒ 3(1 – r) = 1 + r

⇒ r = `1/2`

From (1) a = `4(1 - 1/2)` = 2

G.P. is `2, 1, 1/2, 1/4, .........`