Question

The next term of the A.P. $\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32},....$

• A. $\sqrt{50}$
• B. $\sqrt{46}$
• C. $\sqrt{72}$
• D. None of these

Answer 1

The correct option is A $\sqrt{50}$

$\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32},....$
$\sqrt{2},2\sqrt{2},3\sqrt{2},4\sqrt{2},....$
$a=\sqrt{2},d=2\sqrt{2}-\sqrt{2}=\sqrt{2}$
$t_5=a+(5-1)d=a+4d$
$=\sqrt{2}+4\sqrt{2}=5\sqrt{2}$
$t_5=\sqrt{25}\times \sqrt{2}=\sqrt{50}$