Question

Очень срочно!!! Чому дорівнює сума сорока перших членів арифметичної прогресії (хn), якщо x8= -14, Х30 = -3?

Answer 1

$\displaystyle\bf x_{n} = x_{1} + (n - 1)d \\ \displaystyle\bf\\\left \{ {{x_{8} = - 14} \atop {x_{30} = - 3 }} \right. \\ \displaystyle\bf\\\left \{ {{x_{1} + 7d = - 14\:\: |\times (-1)} \atop {x_{1} + 29d = - 3}} \right. \\ \displaystyle\bf\\ + \left \{ {{ - x_{1} - 7d = 14} \atop {x_{1} + 29d = - 3 }} \right. \\  \\ 29d - 7d = 14 - 3\\ 22d = 11 \\ d = 11\div 22 \\ d = 0.5 \\  \\ x_{1} + 7 \times 0.5 = - 14 \\ x_{1} + 3.5 = - 14 \\ x_{1} = - 14- 3.5 \\ x_{1} = - 17.5 \\  \\ x_{40} = x_{1} + 39d = - 17.5 + 39 \times 0.5= \\ = - 17.5 + 19.5 = 2 \\  \\ S_{n} =  \frac{x_{1} + x_{n}}{2} n \\ S_{40} =  \frac{x_{1} + x_{40}}{2} \times 40 = 20(x_{1} + x_{40}) = \\ = 20 \times ( - 17.5 + 2) = 20 \times - 15.5 = - 310$