Question

Find the ${18}^{th}$ term of the A.P., $\sqrt{2},3\sqrt{2},5\sqrt{2}$.....

• A. $36\sqrt{2}$
• B. $35\sqrt{2}$
• C. $34\sqrt{2}$
• D. $33\sqrt{2}$

Answer 1

The correct option is B $35\sqrt{2}$

Here $a=\sqrt{2}$ and $d=3\sqrt{2}-\sqrt{2}=2\sqrt{2}$.
The nth term of the AP is $a_n=a+(n-1)d$
$\therefore a_{18}=a+17d$

$=\sqrt{2}+17\times 2\sqrt{2}$

$=35\sqrt{2}$