В геометрической прогрессии {a_n} a_4=12. Найдите a_2*a_6.

\[a_{4} = 12 \Longrightarrow a_{4} = b_{1}q^{3}\]

\[a_{2} = b_{1}q;\ \ a_{6} = b_{1}q^{5}\]

\[a_{2} \cdot a_{6} = b_{1}q \cdot b_{1}q^{5} = b_{1}^{2} \cdot q^{6} =\]

\[= \left( b_{1}q^{3} \right)^{2} = \left( a_{4} \right)^{2} = 12^{2} = 144\]

\[Ответ:144.\]