Question

If the sum of an infinite GP be 9 and sum of first two terms be 5 then their common ratio is ______.

Options

• `1/3`

• 3

• `2/3`

• `3/2`

Answer 1

If the sum of an infinite GP be 9 and sum of first two terms be 5 then their common ratio is `underline(2/3)`.

Explanation:

We have,

Sum of infinite GP, `"a"/(1 - "r") = 9`

⇒ a = 9(1 - r)    .....(i)

and sum of first two terms of a GP in 5

⇒ a + ar = 5

⇒ a(1 + r) = 5

⇒ 9(1 - r)(1 + r) = 5

⇒ `1 - "r"^2 = 5/9`

`=> "r"^2 = 4/9`

⇒ r = `2/3`