Найдите первый член и разность арифметической прогрессии, если: a_4+a_8=35; a_3+a_21=65.

\[a_{4} + a_{8} = 35;\ \ a_{3} + a_{21} = 65\]

\[a_{1} + 3d + a_{1} + 7d = 35\]

\[2a_{1} + 10d = 35\]

\[2a_{1} = 35 - 10d;\]

\[a_{1} + 2d + a_{1} + 20d = 65\]

\[2a_{1} + 22d = 65\]

\[2a_{1} = 65 - 22d;\]

\[35 - 10d = 65 - 22d\]

\[12d = 30\]

\[d = \frac{30}{12} = \frac{5}{2} = 2,5.\]

\[2a_{1} = 35 - 10d = 35 - 25 = 10\]

\[a_{1} = 5.\]