Вправи до параграфів: §.19 (1)

1. У геометричній прогресії (b_n) знайдіть член bn, якщо:

1. b₁ = 4, b₂ = 12, n = 3.

b_n = b₁ • q^n–1

q = b2b1 = 124 = 3.

b₃ = 4 • 3² = 36.

2. b₁ = 581, b₂ = 527, n = 7.

q = b2b1 = 5 •8127 •5 = 3.

b₇ = b₁ • q⁶ = 581 • 3⁶ = 534 • 3⁶ = 5 • 3² = 45.

3. b₄ = 3, b₅ = –6, n = 10, b_n – ?.

q = b5b4 = -63 = –2.

b₄ = b₁ • q³

b₁ • (–2)³ = 3.

b₁ = 3-8 = –38

b₁₀ = b₁ • q⁹ = –38 • (–2)⁹ = –38 • (–512) = 192.

4. b₇ = 32, b₈ = 3, n = 16.

q = 323 = 2. b₁₆ = b₁ • q¹⁵.

b₇ = b₁q⁶; 32 = b₁ • 2⁶; b₁ = 32 •8 = 382 = 3216.

b₁₆ = 3216 • 2¹⁵ = 3 • 21616 = 3 • 2824 = 3 • 2⁴ = 48.