Решебник по алгебре 9 класс Мерзляк Задание 875

\[\boxed{\mathbf{875\ (875).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[\left\{ \begin{matrix} x_{3} = 24\ \ \\ x_{8} = 768 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x_{1}q^{2} = 24 \\ x_{1}q^{7} = 768 \\ \end{matrix}\text{\ \ }(\ :)\ \right.\ \text{\ \ \ \ \ \ }\]

\[\text{\ \ }\frac{x_{1}q^{2}}{x_{1}q^{7}} = \frac{24}{768}\text{\ \ }\]

\[\frac{1}{q^{5}} = \frac{24}{768}\]

\[q^{5} = \frac{768}{24}\text{\ \ }\]

\[q^{5} = 32 \Longrightarrow \ \ q = 2\]

\[x_{1} = \frac{24}{q^{2}} = \frac{24}{4} = 6\]

\[S_{7} = \frac{6 \cdot \left( 2^{7} - 1 \right)}{2 - 1} =\]

\[= 6 \cdot (128 - 1) =\]

\[= 6 \cdot 127 = 762.\]

\[Ответ:762.\]