Question

Qual a soma dos multiplos de 9 que estao entre 100 e 1000?

Answer 1

a1 = 108
an = 999
r = 9

an = a1 + (n-1) * r
999 = 108 + (n-1) * 9
999 = 108 + 9n - 9
9n = 999 - 108 + 9
9n = 900
n = 900 / 9
n = 100

Sn = (a1 + an) * n / 2 
S100 = (108 + 999) * 100 / 2
S100 = 1107 * 100 / 2
S100 = 1107 * 50
S100 = 55 350