Question

encontre a soma dos 50 primeiros termos da pa 20 40 60

Answer 1

Primeiro vamos achar a Razão:

$\mathtt{R = A_2 - A_1} \\ \mathtt{R = 40-20} \\ \mathtt{R = 20}$

Agora vamos achar o ultimo termo, 50

$\mathtt{A_n = A_1 + (n-1)~.~R} \\ \mathtt{A_{50} =20 + (50-1)~.~20} \\ \mathtt{A_{50} =20 + 49~.~20} \\ \mathtt{A_{50} =20 + 980} \\ \mathtt{A_{50} =1.000}$

Agora aplicaremos a soma de P.A

$\mathtt{S_n = \dfrac{(A_1 + A_n)~.~n}{2}} \\ \\ \\ \mathtt{S_5_0 = \dfrac{(20 + 50)~.~50}{2}~~=~~ \dfrac{70~.~50}{2}~~=~~\dfrac{3.500}{2}~~=~~1.750} \\ \\ \\ \boxed{\boxed{\mathtt{Resposta: 1.750}}}$