Question

The 4^th term of a G.P. is 16 and the 7^th term is 128, then its common ratio is equal to ______.

Options

• 2

• −2

• 1

• −1

Answer 1

The 4^th term of a G.P. is 16 and the 7^th term is 128, then its common ratio is equal to 2.

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 a G.P. is 16.

⇒ a₄ = 16

⇒ ar^{4 − 1} = 16

⇒ ar³ = 16   .........(1)

Given,

7^th term of a G.P. is 128.

⇒ a₇ = 128

⇒ ar^{7 − 1} = 128

⇒ ar⁶ = 128 .........(2)

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

⇒ `(ar^6)/(ar^3) = 128/16`

⇒ r³ = 8

⇒ r³ = 2³

⇒ r = 2