Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 979

\[\left( a_{n} \right) - арифметическая\ \]

\[прогрессия:\]

\[a_{1} + a_{2} + a_{3} = 0;\]

\[a_{1} + a_{2} + a_{3} + a_{4} = 1.\]

\[1)\ a_{1} + a_{2} + a_{3} = 0\]

\[a_{1} + \left( a_{1} + d \right) + \left( a_{1} + 2d \right) = 0\]

\[3a_{1} + 3d = 0\]

\[a_{1} + d = 0\]

\[a_{1} = - d.\]

\[2)\ a_{1} + a_{2} + a_{3} + a_{4} = 1\]

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

\[4a_{1} + 6d = 1\]

\[- 4d + 6d = 1\]

\[2d = 1\]

\[d = 0,5;\ \ \ \]

\[a_{1} = - 0,5.\]

\[3)\ S_{12} = \frac{2a_{1} + d(n - 1)}{2} \bullet n =\]

\[= \frac{2 \bullet ( - 0,5) + 0,5(12 - 1)}{2} \bullet 12 =\]

\[= ( - 1 + 6 - 0,5) \bullet 6 =\]

\[= 4,5 \bullet 6 = 27.\]

\[Ответ:\ \ 27.\]