The common ratio of a G.P., whose 4^th term is 27 and 6^th term is 243; is :

1. 9

2. 3

3. $\dfrac{1}{3}$

4. $\dfrac{1}{9}$

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 :

$\Rightarrow \dfrac{ar^5}{ar^3} = \dfrac{243}{27} \\[1em] \Rightarrow r^2 = 9 \\[1em] \Rightarrow r = \sqrt{9} = 3.$

Hence, Option 2 is the correct option.