Відповіді §.19 - §.20 » §.19 (1)

У геометричній прогресії (bn) знайдіть член bn, якщо: 1. b1 = 4, b2 = 12, n = 3. bn = b1 • qn–1 q = b_2/b_1 = 12/4 = 3. b3 = 4 • 32 = 36. 2. b1 = 5/81, b2 = 5/27, n = 7. q = b_2/b_1 = (5 •81)/(27 •5) = 3. b7 = b1 • q6 = 5/81 • 36 = 5/3^4 • 36 = 5 • 32 = 45. 3. b4 = 3, b5 = –6, n = 10, bn – ?. q = b_5/b_4 = (-6)/3 = –2. b4 = b1 • q3 b1 • (–2)3 = 3. b1 = 3/(-8) = –3/8 b10 = b1 • q9 = –3/8 • (–2)9 = –3/8 • (–512) = 192. 4. b7 = 3/√2, b8 = 3, n = 16. q = (3√2)/3 = √2. b16 = b1 • q15. b7 = b1q6; 3/√2 = b1 • √26; b1 = 3/(√2 •8) = 3/(8√2) = (3√2)/16. b16 = (3√2)/16 • √215 = (3 • √(2^16 ))/16 = (3 • 2^8)/2^4 = 3 • 24 = 48.