Question

Dada a P.A. (2,4,6,...40)
A soma dos 20 primeiros números pares positivos é:

A)400
B)420
C)440
D)800

Answer 1

P.A (2, 4, 6, ...40)

a₁ = 2
a₂ = 4

r = a₂ - a₁ = 4 - 2 = 2

an = a₁ + (n - 1)*r
a₂₀ = a₁ + (20 - 1)*r
a₂₀ = 2 + 19*2
a₂₀ = 2(1 + 19)
a₂₀ = 2*20
a₂₀ = 40

Sn = (a₁ + an)* n / 2
S₂₀ = (a₁ + a₂₀) * 20 / 2
S₂₀ = (a₁ + a₂₀) * 10
S₂₀ = (2 + 40) * 10
S₂₀ = 42*10
S₂₀ = 420

Answer 2

an=a1+(n-1)r
an=2+(20-1)2
an=2+19*2
an=2+38
an=40
a20=40

sn=(a1+an)n/2
sn=(2+40)*10
sn=42*10
sn=420

alternativa b