If the first term of an A.P. is 2 and the sum of first five terms is equal to one fourth of the sum of the next five terms, then the sum of the first 30 terms is

Common difference $=d$

As per the given condition

$\left(a+a+d+a+2d+a+3d+a+4d\right)=\frac{1}{4}\left(a+5d+a+6d+a+7d+a+8d+a+9d\right)$ $5a+10d=\frac{1}{4}\left(5a+35d\right)$

$5d=-15a$

$5d=-15\times 2$

$d=-6$

$S_{30}=\frac{30}{2}\left[2a+\left(30-1\right)d\right]$

$=15\left(4+\left(29\right)\left(-6\right)\right)$

$=15\left(4-174\right)$

$=-15\times 170$

$=-2550$