Question

15.2 задана геометрическая прогрессия (bn). Найдите:​

Answer 1

Ответ:

1) b₇ = 9/2048

2) b₅ = 1/4

3) b₈ = 4/78125

4) b₉ = -1/625

Объяснение:

Формула нахождения n-го члена геометрической прогрессии:

bₙ = b₁ ∙ qⁿ⁻¹

Применив ее, найдем:

1) b₇ = 18 ∙ (1/4)⁷⁻¹ = 18 ∙ (1/4)⁶ = 18 ∙ 1⁶/4⁶ = 2 ∙ 9 ∙ 1/4096 = 9/2048

2) b₅ = 64 ∙ (1/4)⁵⁻¹ = 64 ∙ (1/4)⁴ = 4³ ∙ 1⁴/4⁴ = 1/4

3) b₈ = 4 ∙ (1/5)⁸⁻¹ = 4 ∙ (1/5)⁷ = 4 ∙ 1⁷/5⁷ = 4 ∙ 1/78125 = 4/78125

4) b₉ = -625 ∙ (-1/5)⁹⁻¹ = -625 ∙ (-1/5)⁸ = -(5)⁴ ∙ 1⁸/5⁸ = -1/5⁴ = -1/625

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