ГДЗ по алгебре 9 класс Макарычев Задание 653

\[\boxed{\text{653\ (}\text{с}\text{).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ b_{7} = 72,9;\ \ \ q = 1,5:\]

\[b_{7} = b_{1}q^{6},\ \ 72,9 = b_{1} \cdot (1,5)^{6},\ \ b_{1} = 6,4;\]

\[S_{7} = b_{1} \cdot \frac{{1,5}^{7} - 1}{1,5 - 1} = \frac{102,95}{0,5} = 205,9.\]

\[\textbf{б)}\ b_{5} = \frac{16}{9};\ \ \ q = \frac{2}{3}:\ \ \]

\[b_{5} = b_{1}\ q^{4} = \frac{2}{3},\ \ \frac{16}{9} = b_{1} \cdot \frac{16}{81},\ \ b_{1} = 9,\]

\[S_{7} = 9 \cdot \frac{\left( \frac{2}{3} \right)^{6} - 1}{\frac{2}{3} - 1} = 9 \cdot \frac{\frac{128}{2187} - 1}{- \frac{1}{3}} = \frac{2059}{81} = 25\frac{34}{81}.\]