Question

Calcule a soma dos 150 primeiros termos da P.A. (2, 6, 10,...).

Answer 1

Primeiramente, vamos encontrar a razão e o 150° termo

$r=a_2-a_1\\\\ r=6-2\\\\ \boxed{r=4}$

150° termo

$a_1_5_0=a_1+149r\\\\ a_1_5_0=2+149*4\\\\ a_1_5_0=2+596\\\\ \boxed{a_1_5_0=598}$

Agora, a soma

$S_1_5_0=\frac{(2+598)*150}{2}\\\\ S_1_5_0=600*75\\\\ \boxed{S_1_5_0=45000}$

Answer 2

an=a1+(n-1).r
a150=2+149.4
a150=2+596
a150=598
 prontinho :)