В геометрической прогрессии {a_n} a_7=-14. Найдите a_5*a_9.

\[a_{7} = - 14 \Longrightarrow a_{7} = a_{1}q^{6}\]

\[a_{5} = a_{1}q^{4}\]

\[a_{9} = a_{1}q^{8}\]

\[a_{5} \cdot a_{9} = a_{1}q^{4} \cdot a_{1}q^{8} =\]

\[= a_{1}^{2} \cdot q^{12} = \left( a_{1}q^{6} \right)^{2} = \left( a_{7} \right)^{2} =\]

\[= ( - 14)^{2} = 196\]

\[Ответ:196.\]