Найдите первый член и разность арифметической прогрессии (an), если: a5+a13=38 и a4+a8=29.

\[a_{5} + a_{13} = 38;\ \ \ a_{4} + a_{8} = 29:\]

\[\left\{ \begin{matrix} a_{1} + 4d + a_{1} + 12d = 38 \\ a_{1} + 3d + a_{1} + 7d = 29\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 2a_{1} + 16d = 38 \\ 2a_{1} + 10d = 29 \\ \end{matrix} \right.\ \text{\ \ }( - )\text{\ \ \ }\]

\[\left\{ \begin{matrix} 6d = 9\ \ \ \ \ \ \ \ \ \ \ \ \\ a_{1} = 19 - 8d \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} d = 1,5\ \ \ \ \ \ \ \ \ \ \ \\ a_{1} = 19 - 12 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} d = 1,5 \\ a_{1} = 7\ \ \\ \end{matrix} \right.\ \]

\[Ответ:d = 1,5;\ \ \ a_{1} = 7.\]