Найдите сумму восемнадцати первых членов арифметической прогрессии (an), если a11-a3-a8=27 и a6+a14=86.

\[\left\{ \begin{matrix} a_{11} - a_{3} - a_{8} = 27 \\ a_{6} + a_{14} = 86\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} d - a_{1} = 27\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 18d + 2a_{1} = 86\ \ \ \ |\ :2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} d - a_{1} = 27\ \ \\ 9d + a_{1} = 43 \\ \end{matrix} \right.\ \text{\ \ \ }( + )\ \]

\[\left\{ \begin{matrix} 10d = 70\ \ \ \ \ \ \\ a_{1} = d - 27 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} d = 7\ \ \ \ \ \ \ \ \\ a_{1} = - 20 \\ \end{matrix} \right.\ \]

\[S_{18} = \frac{2a_{1} + 17d}{2} \cdot 18 =\]

\[= \left( 2a_{1} + 17d \right) \cdot 9 =\]

\[= ( - 40 + 119) \cdot 9 =\]

\[= 79 \cdot 9 = 711.\]

\[Ответ:711.\]