Question

Intr-o progresie geometrica
b8= 12 q=3
Calculati b5 b6 b7 b9 b10 b11

Answer 1

bn = b1 * q^(n-1)

b8 = b1 * q^7

12 = b1 * 3^7

2^2 * 3 = b1 * 3^7

b1 = 2^2 * 3/3^7 = 2^2/3^6 = 4/729

Atunci:

b5 = b1 * q^4 = 4/729 * 3^4 = 4/729 * 81 = 4/9

b6 = b5 * q = 4/9 * 3 = 4/3

b7 = b6 * q = 4/3 * 3 = 4

b9 = b8 * q = 12 * 3 = 36

b10 = b9 * q = 36 * 3 = 108

b11 = b10 * q = 108 * 3 = 324

Answer 2

Răspuns

bn = b₁ · qⁿ⁻¹ formula termenului general, progresie geometrica

b₈ = b₁ · q⁷;  12 = b₁ · q⁷⇒    12 = b₁ · 3⁷⇒ b₁ = 12 : 3⁷ = (3·4 ):3⁷ = 4:3⁶ = 4:729

b₁ = 4:3⁶

Deci b₅ = b₁ · q⁴ = (4:3⁶ ) · 3⁴ = 4:3² = 4/9

b⁶ = b₁ · q⁵ = b₅ · q = (4/9)·3 = 4/3    

b₇ = b₆  · q = (4/3)  · 3 = 4

b⁹ = b₈ · q = 12 · 3 = 36

b₁₀ = b₉ · q = 36 · 3 = 108

b₁₁ = b₁₀ · q = 108 · 3 = 324