Question

The common ratio of a GP., whose 4th term is 27 and 6th term is 243; is ______.

Options

• 9

• 3

• `1/3`

• `1/9`

Answer 1

The common ratio of a GP., whose 4th term is 27 and 6th term is 243; is 3.

Explanation:

Let first term of G.P. be a and common ratio be r.

By formula,

⇒ a_n = ar^{n − 1}

Given,

4^th term of G.P. is 27.

⇒ a₄ = 27

⇒ ar^{4 − 1} = 27

⇒ ar³ = 27 ........(1)

Given,

6^th term of G.P. is 243.

⇒ a₆ = 243

⇒ ar^{6 − 1} = 243

⇒ ar⁵ = 243 ........(2)

Dividing equation (2) by (1), we get:

⇒ `(ar^3)/(ar^5​) = 243/27`

⇒ r² = 9

⇒ r = `sqrt9​`

r = 3