Question

What is the next term of the AP $\sqrt{2},\sqrt{8},\sqrt{18},$ ____?

• A. $\sqrt{24}$
• B. $\sqrt{28}$
• C. $\sqrt{30}$
• D. $\sqrt{32}$

Answer 1

The correct option is D $\sqrt{32}$

We are given a series : $\sqrt{2},\sqrt{8},\sqrt{18}$

$a=\sqrt{2}$

$a+d=\sqrt{8}=\sqrt{4.2}=2\sqrt{2}$

so, $d=2\sqrt{2}-\sqrt{2}=\sqrt{2}$

so, $4^{th}$ term will be

$a+3d=\sqrt{2}+3\sqrt{2}=4\sqrt{2}$

$a+3d=\sqrt{4^2.2}=\sqrt{16.2}=\sqrt{32}$

so, the next term will be $\sqrt{32}$