Question

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

Answer 1

It is given that,

$a_1=\sqrt{2}$

$a_2=3\sqrt{2}$

$a_3=5\sqrt{2}$

This shows that the $n^{th}$ term will be,

$a_n=\left(2n-1\right)\sqrt{2}$

Therefore, ${18}^{th}$ term will be,

$a_{18}=\left(2\left(18\right)-1\right)\sqrt{2}$

$=35\sqrt{2}$