There's a difference of 13 between consecutive terms in the sequence, so that the [tex]n[/tex]-th term of the sequence is
[tex]a_n=4+13(n-1)=13n-9[/tex]
Then the sum of the first 100 terms of the sequence is
[tex]S_{100}=\displaystyle\sum_{n=1}^{100}(13n-9)=13\sum_{n=1}^{100}n-9\sum_{n=1}^{100}1[/tex]
[tex]S_{100}=13\dfrac{100\cdot101}2-9\cdot100[/tex]
[tex]\boxed{S_{100}=64,750}[/tex]
