ГДЗ по алгебре 9 класс Макарычев Задание 696

\[\boxed{\text{696}\text{\ (696)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[S_{10} = 100,\ \ S_{30} = 900,\]

\[S_{10} = \frac{2a_{1} + 9d}{2} \cdot 10 = 5 \cdot \left( 2a_{1} + 9d \right) = 100 \Longrightarrow 2a_{1} + 9d = 20,\]

\[S_{30} = \frac{2a_{1} + 29d}{2} \cdot 30 = 15 \cdot \left( 2a_{1} + 29d \right) = 900 \Longrightarrow 2a_{1} + 29d = 60,\]

\[\left\{ \begin{matrix} 2a_{1} + 9d = 20\ \ \\ 2a_{1} + 29d = 60 \\ \end{matrix} \right.\ -\]

\[\left\{ \begin{matrix} 2a_{1} + 9d = 20 \\ 20d = 40\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} d = 2 \\ a_{1} = 1 \\ \end{matrix} \right.\ \]

\[S_{40} = \frac{2a_{1} + 39d}{2} \cdot 40 = 20 \cdot (2 + 39 \cdot 2) = 1600.\]