Question

calcular a soma dos 200 primeiros numeros termos a pa(1,3,5)

Answer 1

$a_{200}=a_1+199r\\ \\ a_{200}=1+2*199\\ \\ a_{200}=399\\ \\ S_{200}=\frac{200(a_1+a_{200})}{2}\\ \\ S_{200}=100(1+399)=100.400=40.000$

Answer 2

(1,3,5,...)

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

$S_{200}=\dfrac{(a_1+a_{200})\cdot200}{2}$

$r=a_2-a_1=3-1=2$

$a_n=a_1+(n-1)r$

$a_{200}=1+(200-1)\cdot2~~\Rightarrow~~a_{200}=1+199\cdot2~~\Rightarrow~~a_{200}=1+398~~\Rightarrow~~a_{200}=399$.
$S_{200}=\dfrac{(1+399)\cdot200}{2}=\dfrac{400\cdot200}{2}=40~000$.