The series can be clubbed into two AP's, (1 + 7 + 13......) and (4 + 5 + 6.......). So, we can observe that the series can be taken as two AP's by simple rearrangement of numbers. Now, we can find the Sum of 50 terms for each AP formed.

Formula for sum of first n terms of AP is:$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$

So, for first AP
$S_1=\frac{50}{2}(2+49\times 6)=7400$
and similarly,
$S_2=\frac{50}{2}(8+49)=1425$
So, Sum of first 100 terms
$=7400+1425=8825$