\[S_{6} = \frac{b_{1}\left( q^{6} - 1 \right)}{q - 1}\]
\[b_{1} = 16;\ \ q = - \frac{1}{2}:\]
\[S_{6} = \frac{16 \cdot \left( \frac{1}{64} - 1 \right)}{- \frac{1}{2} - 1} = \frac{16 \cdot \frac{63}{64}}{\frac{3}{2}} =\]
\[= \frac{16 \cdot 63 \cdot 2}{3 \cdot 64} = \frac{21}{2} = 10,5.\]