\[S_{n} = 3n^{2} + 7n;\ \ \]
\[S_{2} = 3 \cdot 4 + 7 \cdot 2 = 26;\ \ \]
\[S_{4} = 3 \cdot 16 + 28 = 76\]
\[\left\{ \begin{matrix} a_{1} + a_{1} + d = 26 \\ \frac{2a_{1} + 3d}{2} \cdot 4 = 76 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 2a_{1} + d = 26\ \ \\ 2a_{1} + 3d = 38 \\ \end{matrix} \right.\ \text{\ \ \ }( - )\text{\ \ }\]
\[\ \left\{ \begin{matrix} - 2d = - 12\ \ \ \ \ \ \ \ \ \ \ \\ a_{1} = (26 - d)\ :2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} d = 6\ \ \ \ \\ a_{1} = 10 \\ \end{matrix} \right.\ \]
\[Ответ:\ \ a_{1} = 10;\ \ d = 6.\]