Решебник по алгебре 9 класс Макарычев Задание 569

 

\[\boxed{\text{569}\text{\ (569)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ a_{1} = 1;a_{n + 1} = a_{n} + 1\]

\[a_{2} = a_{1} + 1 = 2,\ \ \]

\[a_{3} = a_{2} + 1 = 3,\]

\[a_{4} = a_{3} + 1 = 4,\ \ \]

\[a_{5} = a_{4} + 1 = 5.\]

\[\textbf{б)}\ a_{1} = 1000;\ \ \ \ \ a_{n + 1} = 0,1a_{n}\text{\ \ }\]

\[a_{2} = 0,1 \cdot a_{1} = 100,\ \ \]

\[a_{3} = 0,1 \cdot a_{2} = 10,\]

\[a_{4} = 0,1 \cdot a_{3} = 1,\ \ \]

\[a_{5} = 0,1 \cdot a_{4} = 0,1.\]

\[\textbf{в)}\ a_{1} = 16;\ \ a_{n + 1} = - 0,5a_{n}\ \]

\[a_{2} = - 0,5 \cdot a_{1} = - 8,\ \ \]

\[a_{3} = - 0,5 \cdot a_{2} = 4,\]

\[a_{4} = - 0,5 \cdot a_{3} = - 2,\ \ \]

\[a_{5} = - 0,5 \cdot a_{4} = 1.\]

\[\textbf{г)}\ a_{1} = 3;\ \ a_{n + 1} = a_{n}^{- 1}\text{\ \ }\]

\[a_{2} = a_{1}^{- 1} = \frac{1}{3},\ \ \]

\[a_{3} = a_{2}^{- 1} = 3,\ \ \]

\[a_{4} = a_{3}^{- 1} = \frac{1}{3},\]

\[a_{5} = a_{4}^{- 1} = 3.\]

\[\boxed{\text{569.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[S_{n} = \frac{\left( a_{1} + a_{n} \right)}{2} \cdot n;\]

\[\textbf{а)}\ a_{1} = 3;\ \ a_{60} = 57:\]

\[S_{60} = \frac{(3 + 57)}{2} \cdot 60 = 60 \cdot 30 =\]

\[= 1800.\]

\[\textbf{б)}\ a_{1} = - 10,5;\ \ a_{60} = 51,5:\]

\[S_{60} = \frac{( - 10,5 + 51,5) \cdot 60}{2} =\]

\[= 41 \cdot 30 = 1230.\]