ГДЗ по алгебре 9 класс Макарычев Задание 685

\[\boxed{\text{685}\text{\ (685)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ a_{1} = 2,\ \ a_{2} = 6,\ \ d = a_{2} - a_{1} = 4,\]

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

\[198 = 2 + 4n - 4\]

\[4n = 200\]

\[n = 50;\]

\[S_{50} = \frac{a_{1} + a_{50}}{2} \cdot n = \frac{2 + 198}{2} \cdot 50 = 100 \cdot 50 = 5000.\]

\[\textbf{б)}\ a_{1} = 95,\ \ a_{2} = 85,\ \ d = a_{2} - a_{1} = - 10,\ \]

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

\[- 155 = 95 - 10n + 10\]

\[10n = 260\]

\[n = 26;\]

\[S_{26} = \frac{a_{1} + a_{26}}{2} \cdot n = \frac{95 - 155}{2} \cdot 26 = - 60 \cdot 13 = - 780.\]