Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 427

\[\boxed{\mathbf{427}.}\]

\[1)\ S_{n} = 30;\ q = \frac{1}{5}\ :\]

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

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

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

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

\[Ответ:\ \ 24.\]

\[2)\ S = 30;\ b_{1} = 20:\]

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

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

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

\[20 = 30 - 30q;\]

\[30q = 10;\]

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

\[Ответ:\ \ \frac{1}{3}.\]