Решебник по алгебре 9 класс Макарычев Задание 593

\[\boxed{\text{593}\text{\ (593)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x_{1} = 8,7;\ \ d = - 0,3:\]

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

\[= 8,7 - 0,3 \cdot (n - 1) =\]

\[= 8,7 - 0,3n + 0,3 = 9 - 0,3n;\]

\[\textbf{а)}\ x_{n} \geq 0:\ \]

\[9 - 0,3n \geq 0\ \ \]

\[0,3n \leq 9\]

\[n \leq 30\]

\[Ответ:для\ n \leq 30.\]

\[\textbf{б)}\ x_{n} < 0:\ \ \]

\[9 - 0,3n < 0\ \ \]

\[0,3n > 9\ \ \]

\[n > 30\]

\[Ответ:для\ n > 30.\]

\[\boxed{\text{593.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)} - 2;\ - 6;\ldots\ \]

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

\[\ x_{2} = x_{1} \cdot q = 2 \cdot ( - 3) = - 6;\ \]

\[\ q = - 3\]

\[x_{n} = x_{1} \cdot q^{n - 1} = 2 \cdot ( - 3)^{n - 1}\ \]

\[x_{7} = 2 \cdot ( - 3)^{6} = 2 \cdot 729 = 1458.\]

\[\textbf{б)} - 40;\ - 20;\ldots\]

\[x_{1} = - 40;\ \ x_{2} = x_{1} \cdot q = - 20;\ \]

\[\ \ \ - 40q = - 20;\ \ \ \ \ \ q = \frac{1}{2}\]

\[x_{n} = - 40 \cdot (0,5)^{n - 1}\ \]

\[\ x_{7} = - 40 \cdot \left( \frac{1}{2} \right)^{6} = - \frac{40}{64} = - \frac{5}{8}.\]

\[\textbf{в)} - 0,125;\ \ 0,25;\ \ldots\]

\[x_{1} = - 0,125;\ \ \]

\[\ x_{2} = x_{1} \cdot q = 0,25;\ \ \ \]

\[- 0,125q = 0,25;\]

\[q = - 2\ \ \]

\[x_{n} = - 0,125 \cdot ( - 2)^{n - 1}\ \]

\[x_{7} = - 0,125 \cdot ( - 2)^{6} =\]

\[= - 0,125 \cdot 64 = - 8.\]

\[\textbf{г)} - 10;\ \ 10;\ \ldots\]

\[x_{1} = - 10;\ \ \ \ x_{2} = - 10q = 10;\ \ \ \]

\[\ q = - 1\ \]

\[x_{n} = \ - 10 \cdot ( - 1)^{n - 1}\text{\ \ }\]

\[x_{7} = - 10 \cdot ( - 1)^{6} = - 10.\]