Question

Determine a soma dos termos 40 primeiros termos da P.A. (8, 2, -4,...)?

Answer 1

vamos calcular 1° an

$a_n=? \\ a_1=8 \\ n=40 \\ r=2-8=-6 \\ \\ termo ~~geral \\ \\ a_n=a_1+(n-1)r \\ \\ a_n=8+(40-1)(-6) \\ \\ a_n=8+(39)(-6) \\ \\ a_n=8+(-234) \\ \\ a_n=8-234 \\ \\ a_n=-226$ 

agora vamos calcular a soma 

$a_n=-226 \\ a_1=8 \\ n=40 \\ \\termo ~~geral \\ \\ S_n= \frac{(a_1+a_n)n}{2} \\ \\ S_{40}= \frac{(8-226)40}{2} \\ \\ S_{40}= \frac{(-218)\not40^{20}}{\not2} \\ \\ S_{40}=(-218)(20) \\ \\ S_{40}=-4.360$