Question

Sabendo que os extremos são a1= 3/2 e a7 = 1/486, determine os sete termos desta PG crescente.

Answer 1

Resposta:

PG

(3/2, 1/2, 1/6, 1/18, 1/54, 1/162, 1/486)

Explicação passo-a-passo:

Fórmula geral da PG:

aₙ=a₁.qⁿ⁻¹

Do enunciado:

a₁=3/2

a₇=1/486

Substituindo na fórmula geral:

1/486=3/2q⁽⁷⁻¹⁾

2/3.(486)=q⁶

q⁶=1/729

729 | 3

243 | 3

81 | 3

27 | 3

9 | 3

3 | 3

1, 1 | 1

729 = 3 . 3 . 3 . 3 . 3 . 3 = 3⁶

q⁶=1/729

q⁶=1/3⁶

q=1/3

a₂=(3/2).(1/3)⁽²⁻¹⁾=(3/2).(1/3)=1/2

a₃=(3/2).(1/3)⁽³⁻¹⁾=(3/2).(1/3)²=(3/2).(1/9)=1/6

a₄=(3/2).(1/3)⁽⁴⁻¹⁾=(3/2).(1/3)³=(3/2).(1/27)=1/18

a₅=(3/2).(1/3)⁽⁵⁻¹⁾=(3/2).(1/3)⁴=(3/2).(1/81)=1/54

a₆=(3/2).(1/3)⁽⁶⁻¹⁾=(3/2).(1/3)⁵=(3/2).(1/243)=1/162