Question

Find the $18$th term of the AP $\sqrt{2},\sqrt{18},\sqrt{50},\sqrt{98},.....$.

Answer 1

Given: AP is $\sqrt{2},\sqrt{18},\sqrt{50},\sqrt{98},.....$

or $\sqrt{2},3\sqrt{2},5\sqrt{2},7\sqrt{2},....$

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

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

$n^{th}$ term is given by,

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

Put $n=18$

$a_{18}=\sqrt{2}+34\sqrt{2}$

$=35\sqrt{2}$.

The $18$th term of the AP $\sqrt{2},\sqrt{18},\sqrt{50},\sqrt{98},.....$ is $35\sqrt{2}$.