\[\boxed{\text{580}\text{\ (580)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)} - 8;\ - 6,5;\ldots\]
\[a_{1} = - 8;\ \ \ a_{2} = - 6,5;\]
\[d = a_{2} - a_{1} = - 6,5 - ( - 8) =\]
\[= 8 - 6,5 = 1,5;\]
\[a_{n} = - 8 + 1,5 \cdot (n - 1);\]
\[a_{23} = - 8 + 1,5 \cdot (23 - 1) =\]
\[= - 8 + 33 = 25.\]
\[\textbf{б)}\ 11;7;\ldots\ \]
\[a_{1} = 11;\ \ a_{2} = 7;\]
\[d = a_{2} - a_{1} = 7 - 11 = - 4;\]
\[a_{n} = 11 - 4 \cdot (n - 1);\]
\[a_{23} = 11 - 4 \cdot (23 - 1) =\]
\[= 11 - 88 = - 77.\]
\[\boxed{\text{580.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[x_{1} = 5,\ \ d = 10:\]
\[S_{5} = \frac{2x_{1} + d(n - 1)}{2} \cdot 5 =\]
\[= \frac{10 + 10 \cdot 4}{2} \cdot 5 = 25 \cdot 5 =\]
\[= 125\ (м) - глубина\ шахты.\]
\[Ответ:125\ м.\]