Question

calcule a soma dos termos de cada uma das programações geométricas:​

Answer 1

Resposta:

Explicação passo-a-passo:

a)

1/2, 1/6, 1/8

q = a2/a1

q= 1/6 : 1/2

q = 1/6 . 2

q= 2/6 (:2)/(:2)

q = 1/3

Sn = a1.(q^n - 1)/ (q - 1)

S3 = 1/2.[(1/3)^3 - 1]/(1/3 - 1)

S3= 1/2.[1/27 - 1] / (1/3 - 3/3)

S3 = (1/54 - 1/2) / (-2/3)

S3 = (1 - 27)/54 . (-3/2)

S3 = (-26)/54 . (-3/2)

S3 = 26/54 . (3/2)

S3 = 78/108 (:2)/(:2)

S3 = 39/59

R.: 39/59

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b)

1, 1/10, 1/100

q = a2/a1

q = 1/10 : 1

q= 1/10

Sn = a1.(q^n - 1)/ (q - 1)

S3 = [1.(1/10)^3 - 1] / (1/10 - 1)

S3 = [1/1000 - 1] / (1/10 - 10/10)

S3 = [1-1000]/1000 / (- 9/10)

S3 = - 999/1000 .(- 10/9)

S3 = 999/9 . 10/1000 (:10)/(:10)

S3 = 111. 1/100

S3 = 111/100

Resp.: 111/100