ГДЗ по алгебре и начала математического анализа 10 класс Алимов Задание 23

\[\boxed{\mathbf{23}\mathbf{.}}\]

\[S = 30.\]

\[1)\ b_{1},\ если\ q = \frac{1}{5}\ :\]

\[S = \frac{b_{1}}{1 - q} = 30;\]

\[\frac{b_{1}}{1 - \frac{1}{5}} = 30;\]

\[b_{1}\ :\frac{4}{5} = 30;\]

\[b_{1} = 30 \bullet \frac{4}{5} = 6 \bullet 4 = 24;\]

\[Ответ:\ \ 24.\]

\[2)\ q,\ если\ b_{1} = 20\ :\]

\[S = \frac{b_{1}}{1 - q} = 30;\]

\[\frac{20}{1 - q} = 30;\]

\[20 = 30(1 - q);\]

\[20 = 30 - 30q;\]

\[30q = 10;\]

\[q = \frac{10}{30} = \frac{1}{3};\]

\[Ответ:\ \ \frac{1}{3}.\]