Find the next three terms of the sequence :

$\sqrt{5}, 5, 5\sqrt{5}, …….$

Since,

$\dfrac{5}{\sqrt{5}} = \dfrac{5\sqrt{5}}{5} = \sqrt{5}$

Hence, the sequence $\sqrt{5}, 5, 5\sqrt{5}, …….$ is a G.P. with r = $\sqrt{5} \text{ and } a = \sqrt{5}.$

Next three terms are = 4^th, 5^th and 6^th.

We know that n^th term of G.P.,

a_n = ar^{n - 1}

⇒ a₄ = ar^{(4 - 1)}

= ar³

= $\sqrt{5}(\sqrt{5})^3 = \sqrt{5}(5\sqrt{5})$

= 25.

⇒ a₅ = ar^{(5 - 1)}

= ar⁴

= $\sqrt{5}(\sqrt{5})^4 = \sqrt{5}(25)$

= $25\sqrt{5}$.

⇒ a₆ = ar^{(6 - 1)}

= ar⁵

= $\sqrt{5}(\sqrt{5})^5 = \sqrt{5}(25\sqrt{5})$

= 125.

Hence, next three terms of the G.P. are = 25, 25√5 and 125.