Question

1) Dada a PA (-91, -79, ... 77), obtenha a soma dos termos.

Answer 1

Primeiramente, devemos encontrar o número de termos da p.a.

$\boxed{a_n = a_1+(n-1)*r}\\\\ 77 = -91+(n-1)*12\\\\\ 77+91+12 = 12n\\\\\ 12n = 180\\\\ \boxed{n=15}$

Temos 15 termos na P.A., agora calcularemos a soma dos 15 termos...

Mas antes, calcularemos o a15

$a_1_5 = -91+(14*12)\\\\\ a_1_5 = 77$

$\boxed{S_n = \frac{(a_1+a_n)*n}{2}}\\\\\ S_1_5 = \frac{(-91+77)*15}{2}\\\\\ S_1_5 = \frac{(-14)(15)}{2}\\\\\ \boxed{S_1_5 = -105}$