Решебник по алгебре 9 класс Мерзляк Задание 775

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\[\left\{ \begin{matrix} a_{6} + a_{8} - a_{14} = - 17 \\ a_{5} + a_{22} = 101\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} a_{1} + 5d + a_{1} + 7d - a_{1} - 13d = - 17 \\ a_{1} + 4d + a_{1} + 21d = 101\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ }\]

\[\left\{ \begin{matrix} a_{1} - d = - 17\ \ \ | \cdot 2 \\ 2a_{1} + 25d = 101\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 2a_{1} - 2d = - 34 \\ 2a_{1} + 25d = 101 \\ \end{matrix} \right.\ ( - )\text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} - 27d = - 135 \\ a_{1} = d - 17\ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} d = 5\ \ \ \ \ \ \ \ \ \ \ \\ a_{1} = 5 - 17 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} d = 5\ \ \ \ \ \ \ \ \\ a_{1} = - 12 \\ \end{matrix} \right.\ \]

\[S_{20} = \frac{2a_{1} + 19d}{2} \cdot 20 =\]

\[= \frac{2 \cdot ( - 12) + 19 \cdot 5}{2} \cdot 20 =\]

\[= \frac{- 24 + 95}{2} \cdot 20 =\]

\[= 71 \cdot 10 = 710.\]

\[Ответ:710.\]