In an $A.P,$ the first term is  $2$ and the sum of the first five  terms is one – fourth of the next five terms, then ${20}^{th}$ term is

First term $=2$

$\therefore$ The $A.P$ is $2$, $2+d$, $2+2d$, $2+3d$………

Sum of first five terms $=10+10d$

Sum of next five terms $=10+35d$

$\therefore$$10+10d=\frac{1}{4}(10+35d)$

$40+40d=10+35d$

$30=-5d$

$d=-6$

$a_{20}=a+19d$

$=2+19(-6)=2-114$

$=-112$