Question

Write the next term of the AP $\sqrt{2},\sqrt{8}.\sqrt{18},......$

• A. $\sqrt{22}$
• B. $\sqrt{32}$
• C. $\sqrt{52}$
• D. None of these

Answer 1

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

Given sequence $\sqrt{2},\sqrt{8},\sqrt{18},...$

We know that $\sqrt{8}=2\sqrt{2},\sqrt{18}=3\sqrt{2}$

Hence the sequence can be rewritten as $\sqrt{2},2\sqrt{2},3\sqrt{2},...$

Here $a=\sqrt{2},d=2\sqrt{2}-\sqrt{2}=\sqrt{2}$

Therefore next term is $t_4=a+3d=\sqrt{2}+3\sqrt{2}=4\sqrt{2}=\sqrt{32}$

Thus the next term is $4\sqrt{2}or\sqrt{32}$