Question

The tenth term of an A.P. : $\sqrt{2},3\sqrt{2},5\sqrt{2},7\sqrt{2}$, ..... is:

• A. $10\sqrt{2}$
• B. $12$
• C. $19\sqrt{2}$
• D. $11\sqrt{2}$

Answer 1

The correct option is C $19\sqrt{2}$

Given A.P. is $\sqrt{2},3\sqrt{2},5\sqrt{2},7\sqrt{2}....$

Its first term, $a=\sqrt{2}$

Common difference, $d=3\sqrt{2}-\sqrt{2}=2\sqrt{2}$

To find out: The tenth term of the A.P.

We know that, the $n^{th}$ term of an A.P. is $t_n=a+(n-1)d$

$\therefore T_{10}=a+(10-1)d$

$\Rightarrow a+9d$

$\Rightarrow \sqrt{2}+9\left(2\sqrt{2}\right)$

$\Rightarrow \sqrt{2}+18\sqrt{2}$

$\therefore t_{10}=19\sqrt{2}$

Hence, the tenth term of the given A.P. is $19\sqrt{2}$.