\[- 5,5;\ - 5;\ldots\]
\[d = 0,5;\ \ \ \ S_{n} = - 31,5\]
\[S_{n} = \frac{2a_{1} + (n - 1)d}{2} \cdot n\]
\[\frac{- 11 + 0,5n - 0,5}{2} \cdot n = - 31,5\]
\[\frac{(0,5n - 11,5) \cdot n}{2} = - 31,5\]
\[0,5n^{2} - 11,5n = - 63\]
\[0,5n^{2} - 11,5n + 63 = 0\ \ \ \ \ |\ :0,5\]
\[n^{2} - 23n + 126 = 0\]
\[n_{1} = 9;\ \ \ n_{2} = 14\]
\[Ответ:\ \ 9\ или\ 14.\]