Найдите первый член арифметической прогрессии (cn), разность которой равна d, если: c4=7, c9=-8.

\[c_{4} = 7;\ \ c_{9} = - 8:\]

\[\left\{ \begin{matrix} c_{1} + 3d = 7\ \ \ \\ c_{1} + 8d = - 8 \\ \end{matrix}\text{\ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} c_{1} = 7 - 3d\ \ \ \ \ \ \ \ \ \ \ \ \ \\ 7 - 3d + 8d = - 8 \\ \end{matrix}\text{\ \ \ } \right.\ \]

\[\left\{ \begin{matrix} c_{1} = 7 - 3d \\ 5d = - 15\ \ \ \ \\ \end{matrix}\text{\ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} c_{1} = 7 - 3d \\ d = - 3\ \ \ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} c_{1} = 16 \\ d = - 3 \\ \end{matrix} \right.\ \]

\[c_{1} = 16.\]

\[Ответ:16.\]