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