Question

Qual é a soma dos 40 primeiros termos da PA (15,20,25...)

Answer 1

$\{a_1,a_2,a_3,\cdots\}\equiv\{15,20,25,\cdots\}$

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

$a_2=a_1+r\ \to\ r=a_2-a_1=20-15\ \therefore\ \boxed{r=5}$

$a_{40}=a_1+39r=15+39(5)\ \therefore\ \boxed{a_{40}=210}$

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

$S_{40}=\dfrac{40}{2}(15+210)\ \therefore\ \boxed{S_{40}=4500}$