Write the next term of the AP

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, $\mathrm{T}_{4}=a+3 d=2 \sqrt{2}+3 \sqrt{2}=5 \sqrt{2}=\sqrt{50}$

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