Question

Найдите сумму n первых членов арифметической прогрессии: -5; -9; -13;..., если n=17

Answer 1

$d = - 9 - ( - 5) = - 9 + 5 = - 4$

$a_{17} = a_{1} + 16d \\ a_{17} = - 5 + 16 \times ( - 4) = - 5 - 64 = \\ = - 69$

$S_{17} = \frac{a_{1} + a_{17}}{2} \times 17 \\ S_{17} = \frac{ - 5 - 69}{2} \times 17 = \frac{ - 74}{2} \times 17 = - 629$

ответ: -629

Answer 2

$a_{1} = -5\\a_{2} = -9\\d = a_{2} - a_{1} = -9 - (-5) = -9 + 5 = -4\\\\S_{n} = \frac{2a_{1}+d(n-1)}{2}*n\\\\S_{17} = \frac{2*(-5)+16d}{2}*n\\\\S_{17} = \frac{-10-64}{2} * n\\\\S_{17} = \frac{-74*17}{2}\\\\S_{17} = \frac{-1258}{2}\\\\S_{17} = -629$

Ответ: -629