Найдите первый член и разность арифметической прогрессии, в которой S3=60, s7=56.

\[S_{3} = 60;\ \ S_{7} = 56\]

\[S_{3} = \frac{2a_{1} + 2d}{2} \cdot 3 = \left( a_{1} + d \right) \cdot 3\]

\[60 = 3(a_{1} + d)\]

\[a_{1} + d = 20 \rightarrow a_{1} = 20 - d.\]

\[S_{7} = \frac{2a_{1} + 6d}{2} \cdot 7 =\]

\[= 7 \cdot \left( a_{1} + 3d \right)\]

\[56 = 7 \cdot \left( a_{1} + 3d \right)\]

\[a_{1} + 3d = 8 \rightarrow a_{1} = 8 - 3d.\]

\[20 - d = 8 - 3d\]

\[2d = - 12\]

\[d = - 6.\]

\[a_{1} = 20 + 6 = 26.\]

\[Ответ:a_{1} = 26;\ \ d = - 6.\]