Решебник по алгебре 9 класс Мерзляк Задание 1030

\[\boxed{\mathbf{1030\ (1030).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[\left\{ \begin{matrix} a_{3} = 11 \\ a_{7} = 27 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} a_{1} + 2d = 11 \\ a_{1} + 6d = 27 \\ \end{matrix} \right.\ - \ \]

\[\ - 4d = - 16 \Longrightarrow \ \ d = 4,\ \ \]

\[a_{1} = 11 - 2 \cdot 4 = 3\]

\[S_{n} = \frac{2a_{1} + d(n - 1)}{2} \cdot n = 253\]

\[\frac{2 \cdot 3 + 4 \cdot (n - 1)}{2} \cdot n = 253\]

\[\frac{6 + 4 \cdot (n - 1)}{2} \cdot n = 253\]

\[(3 + 2n - 2) \cdot n = 253\]

\[(2n + 1) \cdot n = 253\]

\[2n^{2} + n - 253 = 0\]

\[D = 1 + 2024 = 2025\]

\[n = \frac{- 1 - 45}{4} < 0,\]

\[\ \ n = \frac{- 1 + 45}{4} = 11\]

\[Ответ:n = 11.\]