Question

Find the tenth term of the sequence, $\sqrt{2},\sqrt{8},\sqrt{18}.$

Answer 1

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

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

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

Tenth term$=t_{10}=a+9d=\sqrt{2}+9\times \sqrt{2}=\sqrt{2}+9\sqrt{2}=10\sqrt{2}$

$\therefore$ the tenth term is $10\sqrt{2}$