S4 = b1 * (q³ - 1) /(q - 1) = b1 (q - 1)(q² +q + 1)/(q - 1) =
= b1 * (q² + q + 1) = 40 (1)
b2 = b1*q
b4 = b1*q³
b1*q + b1q³ = 30
b1*q(1 + q²) = 30 (2)
Поделим (1) на (2)
b1 (q2 + q +1) / b1*q (1 + q²) = 40/30
(q² + q + 1) / (q + q²) = 4 / 3
3 (q² + q + 1) = 4 (q + q²)
3q² + 3q + 3 = 4q + 4q²
4q² - 3q² + 4q - 3q - 3 = 0
q² + q - 3 = 0
- 1 + √13 - 1 - √13
q1 = -------------- q 2 = -----------------
2 2