Question

Find the next term of $AP\sqrt{2},\sqrt{8},\sqrt{18}$

Answer 1

next term of $AP$

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

$d=\sqrt{2}$

$d=\sqrt{8}-\sqrt{2}$

$t_n=a+(n-1)d$

$t_4=a+3d=\sqrt{2}+3(\sqrt{8}-\sqrt{2})$

$=\sqrt{2}+3\sqrt{8}-3\sqrt{2}$

$=3\sqrt{8}-2\sqrt{2}$

$=3\sqrt{4\times 2}-2\sqrt{2}$

$=6\sqrt{2}-2\sqrt{2}$

$t_4=4\sqrt{2}$