Question

qual a soma dos termos da p.a (100,95,...20)

Answer 1

a₁ = 100

r = - 5

aₙ = 20

n = ?

aₙ = a1 + (n-1) * r

20 = 100 + (n - 1) * (-5)

20 = 100 + (-5n + 5 )

20 = 100 - 5n + 5

20 - 105 = - 5n

-85 = - 5n

-85/-5 = n

17 = n

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

S₁₇ = (100 + 20) * 17 /2

S₁₇ = (120 * 17)/2

S₁₇ = 2040/2

S₁₇ = 1020