\[8 + 5 + 2 + \ldots + x = - 130\]
\[a_{1} = 8;\ \ a_{2} = 5;\ \ a_{n} = x;\ \ \]
\[S_{n} = - 130:\]
\[d = a_{2} - a_{1} = 5 - 8 = - 3.\]
\[S_{n} = \frac{2a_{1} + d(n - 1)}{2} \cdot n\]
\[\frac{2 \cdot 8 - 3 \cdot (n - 1)}{2} \cdot n = - 130\]
\[(16 - 3n + 3) \cdot n = - 130 \cdot 2\]
\[19n - 3n^{2} = - 260\]
\[3n^{2} - 19n - 260 = 0\]
\[D = 361 + 3120 = 3481 = 59^{2}\]
\[n_{1} = \frac{19 + 59}{6} = \frac{78}{6} = 13;\ \]
\[n_{2} = \frac{19 - 59}{6} =\]
\[= - \frac{40}{6} < 0\ (не\ подходит).\]
\[x = a_{13} = a_{1} + 12d =\]
\[= 8 - 3 \cdot 12 = 8 - 36 = - 28.\]
\[Ответ:x = - 28.\]