Question

Calcule a soma dos 80 primeiros termos da P.A ( -15, -11, -7, -3 ...)

Answer 1

Primeiro, vamos encontrar o a80.

$\boxed{a_n=a_1+(n-1)*r}\\\\ r=-11-(-15) \rightarrow\ 11+15=4\\\\\ a_8_0=-15+(80-1)*4\\\\\ a_8_0=-15+79*4\\\\\ a_8_0=-15+316\\\\ \boxed{a_8_0=301}$

Agora, a somatória:

$\boxed{S_n=\frac{(a_1+a_n)*n}{2}}\\\\\ S_8_0=\frac{(-15+301)*80}{2}\\\\ S_8_0=286*40\\\\ \boxed{S_8_0=11440}$