Решебник по алгебре 9 класс Мерзляк Задание 805

\[\boxed{\mathbf{805\ (805).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ 7 + 13 + 19 + \ldots +\]

\[+ (6n + 1) = 480\]

\[a_{1} = 7,\ \ a_{n} = 6n + 1,\ \ \]

\[S_{n} = 480\]

\[S_{n} = \frac{a_{1} + a_{n}}{2} \cdot n\ \ \]

\[480 = \frac{7 + 6n + 1}{2} \cdot n\]

\[480 = \frac{8 + 6n}{2} \cdot n\]

\[480 = (4 + 3n) \cdot n\]

\[3n^{2} + 4n - 480 = 0\]

\[D = 16 + 5760 = 5776\]

\[n = \frac{- 4 - 76}{6} < 0\ \]

\[n = \frac{- 4 + 76}{6} = 12\]

\[Ответ:\ n = 12.\]

\[2)\ 5 + 8 + 11 + \ldots + x = 124\]

\[a_{1} = 5;\ \ d = 8 - 5 = 3;\ \ \]

\[a_{n} = x;\ \ S_{n} = 124\]

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

\[124 = \frac{2 \cdot 5 + 3 \cdot (n - 1)}{2} \cdot n\]

\[124 = \frac{10 + 3n - 3}{2} \cdot n\]

\[124 = \frac{3n + 7}{2} \cdot n\ \ \ \ \ | \cdot 2\]

\[248 = (3n + 7) \cdot n\]

\[3n^{2} + 7n - 248 = 0\]

\[D = 3025\]

\[n = \frac{- 7 - 55}{6} < 0\ \]

\[n = \frac{- 7 + 55}{6} = 8\]

\[тогда:\ \]

\[a_{n} = a_{1} + d(n - 1) = x\ \ \]

\[x = 5 + 3 \cdot (8 - 1) =\]

\[= 5 + 21 = 26\]

\[Ответ:x = 26.\]