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