ГДЗ по алгебре 9 класс Макарычев Задание 609

\[\boxed{\text{609}\text{\ (609)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ x_{1} = 1,\ x_{2} = 2,\ \ldots,\ x_{150} = 150;\]

\[S_{150} = \frac{(x_{1} + x_{n})}{2} \cdot n = \frac{1 + 150}{2} \cdot 150 = 11\ 325;\ \]

\[\textbf{б)}\ x_{1} = 20,\ \ x_{2} = 21,\ \ x_{n} = 19 + n,\ \ x_{n} = 120;\]

\[19 + n = 120,\ \ n = 101,\]

\[S_{101} = \frac{(x_{1} + x_{n})}{2} \cdot n = \frac{20 + 120}{2} \cdot 101 = 7070;\]

\[\textbf{в)}\ x_{1} = 4,\ \ x_{2} = 8,\ \ x_{n} = 4n,\ \ x_{n} = 300,\ \ \]

\[300 = 4n,\ \ n = 75,\]

\[S_{75} = \frac{(x_{1} + x_{n})}{2} \cdot n = \frac{4 + 300}{2} \cdot 75 = 11\ 400;\]

\[\textbf{г)}\ x_{1} = 7,\ \ x_{2} = 14,\ \ x_{n} = 7n,\ \ 7n \leq 130,\ \ n \leq 18\frac{4}{7};\]

\[n = 18,\ \ x_{n} = 126,\ \ S_{18} = \frac{7 + 126}{2} \cdot 18 = 1197.\]