Решебник по алгебре 9 класс Макарычев Задание 695

\[\boxed{\text{695}\text{\ (695)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ c_{1} = 8,2,\ \ c_{2} = 7,4,\ \ d = c_{2} - c_{1} = - 0,8;\]

\[c_{n} = c_{1} + d(n - 1) = 8,2 - 0,8n + 0,8 = 9 - 0,8n\]

\[9 - 0,8n > 0,\]

\[0,8n < 9\]

\[n < 11,25 \Longrightarrow n = 11.\]

\[S_{11} = \frac{2c_{1} + 10d}{2} \cdot 11 = \frac{16,4 - 8}{2} \cdot 11 = 46,2.\]

\[\textbf{б)}\ c_{1} = - 6,5,\ \ c_{2} = - 6,\ \ d = c_{2} - c_{1} = 0,5,\]

\[c_{n} = c_{1} + d(n - 1) = - 6,5 + 0,5n - 0,5 = 0,5n - 7,\]

\[0,5n - 7 < 0 \Longrightarrow n < 14 \Longrightarrow n = 13,\]

\[S_{13} = \frac{2c_{1} + 12d}{2} \cdot 13 = \left( c_{1} + 6d \right) \cdot 13 = ( - 6,5 + 0,5 \cdot 6) \cdot 13 = - 45,5.\]

\[\boxed{\text{695.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[b_{2} = - \frac{1}{32},\ \ b_{3} = \frac{1}{16},\ \ \]

\[b_{12} = ?\]

\[\left\{ \begin{matrix} b_{2} = b_{1} \cdot q\ \\ b_{3} = b_{1} \cdot q^{2} \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} b_{1} \cdot q = - \frac{1}{32} \\ b_{1} \cdot q^{2} = \frac{1}{16} \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} b_{1} \cdot q = - \frac{1}{32} \\ - \frac{1}{32} \cdot q = \frac{1}{16} \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} q = - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ b_{1} = - \frac{1}{32}\ :q = \frac{1}{64} \\ \end{matrix} \right.\ \]

\[b_{12} = b_{1} \cdot q^{12} = \frac{1}{64} \cdot ( - 2)^{11} =\]

\[= - 32.\]