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

1. 2

2. -2

3. 1

4. -1

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 :

$\Rightarrow \dfrac{ar^6}{ar^3} = \dfrac{128}{16} \\[1em] \Rightarrow r^3 = 8 \\[1em] \Rightarrow r^3 = 2^3 \\[1em] \Rightarrow r = 2.$

Hence, Option 1 is the correct option.