Решебник по алгебре 9 класс Макарычев Задание 649

\[\boxed{\text{649}\text{\ (649)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ 3; - 6;\ldots\ \]

\[b_{1} = 3,\ \ b_{2} = b_{1} \cdot q = - 6,\ \ q = - 2:\]

\[S_{6} = b_{1} \cdot \frac{q^{6} - 1}{q - 1} = 3 \cdot \frac{64 - 1}{- 2 - 1} = 3 \cdot \frac{63}{- 3} = - 63.\]

\[\textbf{б)}\ 54;36;\ldots\ \]

\[b_{1} = 54,\ \ b_{2} = b_{1} \cdot q = 36,\ \ q = \frac{36}{54} = \frac{2}{3}:\]

\[S_{6} = b_{1} \cdot \frac{q^{6} - 1}{q - 1} = 54 \cdot \frac{\left( \frac{2}{3} \right)^{6} - 1}{\frac{2}{3} - 1\ } = 54 \cdot \frac{\frac{64}{729} - 1}{- \frac{1}{3}} = \frac{54 \cdot 3 \cdot 664}{729} =\]

\[= \frac{1330}{9} = 147\frac{7}{9}.\]

\[\textbf{в)} - 32; - 16;\ldots\]

\[b_{1} = - 32,\ \ b_{2} = b_{1} \cdot q = - 16,\ \ q = \frac{1}{2}:\]

\[S_{6} = b_{1} \cdot \frac{q^{6} - 1}{q - 1} = - 32 \cdot \frac{\left( \frac{1}{2} \right)^{6} - 1}{\frac{1}{2} - 1\ } = - 64 \cdot \frac{63}{64} = - 63.\]

\[\textbf{г)}\ 1;\ - \frac{1}{2};\ldots\ \]

\[b_{1} = 1,\ \ b_{2} = b_{1} \cdot q = - \frac{1}{2},\ \ q = - \frac{1}{2}:\]

\[S_{6} = b_{1} \cdot \frac{q^{6} - 1}{q - 1} = \frac{\left( - \frac{1}{2} \right)^{6} - 1}{- \frac{1}{2} - 1} = - \frac{2}{3} \cdot \left( - \frac{63}{64} \right) = \frac{21}{32}.\]

\[\boxed{\text{649.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

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

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

\[\Longrightarrow x_{m} - x_{n} =\]

\[= x_{1} + dm - d - x_{1} - dn + d =\]

\[= dm - dn = d \cdot (m - n)\]

\[\Longrightarrow x_{m} - x_{n} = d \cdot (m - n) \Longrightarrow\]

\[\Longrightarrow d = \frac{x_{m} - x_{n}}{m - n} \Longrightarrow ч.т.д.\]