Решебник по алгебре 9 класс Макарычев Задание 584

\[\boxed{\text{584\ (584).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

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

\[x_{1} = x_{n} - d(n - 1)\]

\[\textbf{а)}\ x_{30} = 128;d = 4:\]

\[x_{1} = x_{30} - d(30 - 1) =\]

\[= 128 - 4 \cdot 29 = 12.\]

\[\textbf{б)}\ x_{45} = - 208;\ \ d = - 7:\ \]

\[x_{1} = x_{45} - d(45 - 1) =\]

\[= - 208 + 7 \cdot 44 = 100.\]

\[\boxed{\text{584.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[x_{1} = 17,\ \ x_{2} = 14,\]

\[\ \ d = x_{2} - x_{1} = 14 - 17 = - 3:\]

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

\[= \frac{34 - 3 \cdot (n - 1)}{2} \cdot n > 0 \Longrightarrow\]

\[\Longrightarrow 34n - 3n^{2} + 3n > 0 \Longrightarrow\]

\[\Longrightarrow 3n^{2} - 37n < 0 \Longrightarrow\]

\[n(3n - 37) < 0\]

\[n_{1} = 0,\ \ n_{2} = 12\frac{1}{3};\]

\[так\ как\ n \in N \Longrightarrow n = 12.\]

\[Ответ:\ \ 12\ членов.\ \]