\[b_{n} = 5 \cdot 2^{n + 1}\]
\[b_{1} = 5 \cdot 2^{2} = 20;\ \ \ \ \]
\[b_{2} = 5 \cdot 2^{3} = 40;\]
\[q = \frac{40}{20} = 2.\]
\[S_{7} = \frac{20 \cdot (128 - 1)}{2 - 1} =\]
\[= 20 \cdot 127 = 2540.\]
\[Ответ:2540.\]