Question:
Write the next term of the AP $\sqrt{8}, \sqrt{18}, \sqrt{32}, \ldots \ldots$
Solution:
The given $\mathrm{AP}$ is $\sqrt{8}, \sqrt{18}, \sqrt{32}, \ldots$
On simplifying the terms, we get:
$2 \sqrt{2}, 3 \sqrt{2}, 4 \sqrt{2}, \ldots$
Here, $a=2 \sqrt{2}$ and $d=(3 \sqrt{2}-2 \sqrt{2})=\sqrt{2}$
$\therefore$ Next term, $\mathrm{T}_{4}=a+3 d=2 \sqrt{2}+3 \sqrt{2}=5 \sqrt{2}=\sqrt{50}$