Найдите сумму бесконечной геометрической прогрессии (bn), если b3=18, b5=2.

\[\left\{ \begin{matrix} b_{3} = 18 \\ b_{5} = 2\ \ \\ \end{matrix}\text{\ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} b_{1}q^{2} = 18 \\ b_{1}q^{4} = 2\ \ \\ \end{matrix}\text{\ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} q^{2} = \frac{1}{9}\text{\ \ \ } \\ b_{1} = \frac{2}{q^{4}} \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} q = \pm \frac{1}{3}\text{\ \ } \\ b_{1} = 162 \\ \end{matrix} \right.\ \]

\[при\ \ q = \frac{1}{3}:\]

\[S = \frac{162}{1 - \frac{1}{3}} = 162\ :\frac{2}{3} = 243.\]

\[при\ q = - \frac{1}{3}:\]

\[S = \frac{162}{1 + \frac{1}{3}} = 162\ :\frac{4}{3} = 121,5.\]

\[Ответ:243\ \ \ или\ \ \ 121,\ 5.\]