Question

Dada a PA (2, 4, 6, 8, 10, …), calcule a soma dos seus 60 primeiros termos: ​

Answer 1

$\{a_1,a_2,a_3,a_4,a_5,\dots\}\equiv\{2,4,6,8,10,\dots\}$

$\boxed{a_n=a_k+(n-k)r}$

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

$a_{60}=a_1+59r=2+59(2)\ \to\ \boxed{a_{60}=120}$

$\boxed{S_n=\dfrac{n}{2}\big(a_1+a_n\big)}$

$S_{60}=\dfrac{60}{2}\big(a_1+a_{60}\big)=30\big(2+120)\ \to\ \boxed{S_{60}=3660}$