Question

Find the 10th term of the sequence $\sqrt{2},\sqrt{8},\sqrt{18}$

Answer 1

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

$=\sqrt{2},2\sqrt{2},3\sqrt{2}$ ,.....

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

[Using formula: $t_n=a+(n-1)d$

$\Rightarrow t_{10}=a+(10-1)d$

$\Rightarrow t_{10}=\sqrt{2}+9\sqrt{2}$

$\Rightarrow t_{10}=10\sqrt{2}$

Hence, tenth term for given sequence is

$10\sqrt{2}$

.