\[4,\ 8,\ 12,\ \ldots,\ 100\]
\[a_{1} = 4;\ \ a_{2} = 8;\ \ a_{n} = 100:\]
\[d = 8 - 4 = 4.\]
\[a_{n} = a_{1} + d(n - 1)\]
\[100 = 4 + 4n - 4\]
\[4n = 100\]
\[n = 25.\]
\[S_{25} = \frac{a_{1} + a_{25}}{2} \cdot 25 =\]
\[= \frac{4 + 100}{2} \cdot 25 = 52 \cdot 25 =\]
\[= 1300.\]