If the (p + q)th and (p − q)th term of a G.P. are m and n respectively, then its pth term is :

1. mn

2. $\sqrt{mn}$

3. (mn)²

4. $\dfrac{m}{n}$

Given,

(p + q)th term = m

(p - q)th term = n

We know that,

nth term of a G.P. is given by,

T_n = ar^{n - 1}

⇒ T_{p + q} = m

⇒ ar^{p + q - 1} = m ……..(1)

⇒ T_{p - q} = n

⇒ ar^{p - q - 1} = n ……..(2)

⇒ T_p = ar_{p - 1}

Multiplying equation (1) and (2) :

⇒ ar^{p + q - 1} × ar^{p - q - 1} = mn

⇒ a².r^{p + q - 1 + p - q - 1} = mn

⇒ a².r^{2p - 2} = mn

Taking square root on both sides:

⇒ $\sqrt{a^2r^{2p - 2}} = \sqrt{mn}$

⇒ ar^{p - 1} = $\sqrt{mn}$

Thus, pth term = $\sqrt{mn}$.

Hence, option 2 is the correct option.