\[\left\{ \begin{matrix} b_{4} = 48 \\ b_{6} = 12 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} b_{1}q^{3} = 48 \\ b_{1}q^{5} = 12 \\ \end{matrix} \right.\ \ \ |\ :\]
\[q^{2} = \frac{12}{48}\ \]
\[q^{2} = \frac{1}{4}\text{\ \ }\]
\[q = \pm \frac{1}{2}.\]
\[\left\{ \begin{matrix} q = \pm \frac{1}{2}\text{\ \ \ \ \ \ } \\ b_{1} = \pm 384 \\ \end{matrix} \right.\ \]
\[S = \frac{384}{1 - \frac{1}{2}} = \frac{384}{0,5} = 768.\]
\[S = \frac{- 384}{1 - ( - 0,5)} =\]
\[= - \frac{384}{1,5} = - 256.\]
\[Ответ:768\ \ или\ \ ( - 256).\]