Найдите сумму десяти первых членов арифметической прогрессии (an), если: a6=45, a14=-43.

\[a_{6} = 45;\ \ \ \ \ a_{14} = - 43:\]

\[\left\{ \begin{matrix} a_{1} + 5d = 45\ \ \ \ \ \ \\ a_{1} + 13d = - 43 \\ \end{matrix}\text{\ \ }( - )\text{\ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} - 8d = 88\ \ \ \ \ \ \ \ \ \ \ \ \\ a_{1} = - 43 - 13d \\ \end{matrix}\text{\ \ \ \ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} d = - 11 \\ a_{1} = 100 \\ \end{matrix} \right.\ \]

\[S_{10} = \left( 2a_{1} + 9d \right) \cdot 5 =\]

\[= (200 - 99) \cdot 5 = 505.\]

\[Ответ:505.\ \]