Question

calcule a soma dos 12 primeiros termos da p.a. (-7, -4, -1, ...).

Answer 1

!° deverá encontrar o valor do último termo:

$PA~(-7, -4, -1, ...)\\\\\\ a_1=-7\\r=-4-(-7)\to -4+7\to 3\\ n=12\\ a_{n}=a_{12}=?\\\\\\ a_n=a_1+(n-1).r\\\\\\ a_{12}=-7+(12-1).3\to\\\\ a_{12}=-7+11.3\to\\\\ a_{12}=-7+33\to\\\\ \large\boxed{a_{12}=+26}\\\\\\\\ PA~(-7, -4, -1, 2, 5, 8, 11, 14, 17, 20, 23, 26)$


Agora calculamos a soma dos termos:

$S_n= \dfrac{(a_1+a_n).n}{2} \\\\S_n= \dfrac{(-7+26).12}{2} \to \\\\ S_n= \dfrac{19.12}{2} \to \\\\ S_n= \dfrac{228}{2} \to \\\\ \large\boxed{\boxed{S_n= 114}}$