Найдите первый член и разность арифметической прогрессии (an), если: a4+a8=35 и a3+a21=65.

\[a_{4} + a_{8} = 35;\ \ \ \ \ a_{3} + a_{21} = 65\]

\[\left\{ \begin{matrix} a_{4} + a_{8} = 35\ \ \\ a_{3} + a_{21} = 65 \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} a_{1} + 3d + a_{1} + 7d = 35\ \ \ \\ a_{1} + 2d + a_{1} + 20d = 65 \\ \end{matrix}\text{\ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} {2a}_{1} + 10d = 35 \\ {2a}_{1} + 22d = 65 \\ \end{matrix} \right.\ ( - )\]

\[\left\{ \begin{matrix} - 12d = - 30\ \ \ \\ a_{1} = \frac{65 - 22d}{2} \\ \end{matrix}\text{\ \ \ \ } \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} d = 2,5 \\ a_{1} = 5\ \ \\ \end{matrix} \right.\ \]

\[Ответ:a_{1} = 5;\ \ \ d = 2,5.\]