Question

calcule a soma dos múltiplos de 7 entre 100 e 1000

Answer 1

a1=105
an=994
r=7
n=?
an=a1 + (n-1)r
994=105+(n-1)7
994=105+7n-7
105+7n-7=994
7n=994+7-105
7n=896
n=896/7
n=128

sn= (a1+an)n/2
Sn= (105+994)*128/2
Sn= (1099)*128/2
Sn=140672/2
Sn=70336

Answer 2

1000 - 100 = 900 ---- 900 ÷ 7 = 128,571 ---- são 128 múltiplos de 7 entre 100

e 1000.


15 . 7 = 105 ------ a₁ = 105

142 . 7 = 994 -----  a₁₂₈ = 994

Sⁿ = [(a₁ + aⁿ) .n]/2 ------- S₁₂₈ = [(105 + 994)128]/2  ---- S₁₂₈ = (1099) . 64

S₁₂₈ = 70336