Найдите первый член и знаменатель геометрической прогрессии (bn), если: b8=25b6 и b2+b4=-520.

\[\left\{ \begin{matrix} b_{8} = 25b_{6}\text{\ \ \ \ \ \ \ \ \ \ \ } \\ b_{2} + b_{4} = - 520 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} b_{1}q^{7} = 25b_{1}q^{5}\text{\ \ \ \ \ \ \ \ \ } \\ b_{1}q + b_{1}q^{3} = - 520 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} q^{2} = 25\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ b_{1}q\left( 1 + q^{2} \right) = - 520 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} q = \pm 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ b_{1}q\left( 1 + q^{2} \right) = - 520 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} q = \pm 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ b_{1} = \frac{- 520}{q\left( 1 + q^{2} \right)} \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} q = 5\ \ \ \ \\ b_{1} = - 4 \\ \end{matrix} \right.\ \ \ \ \ \ \ \ или\ \ \ \ \ \ \left\{ \begin{matrix} q = - 5 \\ b_{1} = 4\ \\ \end{matrix} \right.\ \]

\[Ответ:q = 5;\ b_{1} = - 4\ \ \ или\ \ \]

\[q = - 5;\ b_{1} = 4.\]