ГДЗ по алгебре 9 класс Макарычев Задание 704

\[\boxed{\text{704\ (704).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ x_{n} = 2^{n}\]

\[x_{1} = 2^{1} = 2\]

\[x_{2} = 2^{2} = 4\]

\[x_{3} = 2^{3} = 8\]

\[q = \frac{x_{3}}{x_{2}} = \frac{x_{2}}{x_{1}} =\]

\[= 2 \Longrightarrow геометрическая\ \]

\[прогрессия.\]

\[\textbf{б)}\ x_{n} = 3^{- n}\]

\[x_{1} = 3^{- 1} = \frac{1}{3}\]

\[x_{2} = 3^{- 2} = \frac{1}{9}\]

\[x_{3} = 3^{- 3} = \frac{1}{27}\]

\[q = \frac{x_{3}}{x_{2}} = \frac{x_{2}}{x_{1}} =\]

\[= \frac{1}{3} \Longrightarrow геометрическая\ \]

\[прогрессия.\]

\[\textbf{в)}\ x_{n} = n²\]

\[x_{1} = 1^{2} = 1\]

\[x_{2} = 2^{2} = 4\]

\[x_{3} = 3² = 9\]

\[q = \frac{x_{n}}{x_{n - 1}} = \frac{n^{2}}{(n - 1)^{2}} \Longrightarrow зависит\ \]

\[от\ n,\ не\ геометрическая\ \]

\[прогрессия.\]

\[\textbf{г)}\ x_{n} = ab^{n},\ \ где\ a \neq 0,\]

\[b \neq 0,\]

\[q = \frac{x_{n}}{x_{n - 1}} = \frac{ab^{n}}{ab^{n - 1}} = b^{n - n + 1} =\]

\[= b \Longrightarrow геометрическая\ \]

\[прогрессия.\]