B1 - первый член;
b1q - второй член;
b1q² - третий член;
b1 + b1q + b1q² = 155
b1q² - b1 = 120
b1(1 + q + q²) = 155
b1(q² - 1) = 120
b1 = 155/(1 + q + q²)
b1 = 120/(q² - 1)
155/(1 + q + q²) = 120/(q² - 1)
120q² + 120q + 120 = 155q² - 155
-35q² + 120q + 275 = 0
7q² - 24q + 55 = 0
D = 24² + 55•4•7 = 46²
q1 = (24 + 46)/14 = 5
q2 = (24 - 46)/14 < 0 - не уд. условию
q = 5
b1q² = b1 + 120
q = 5
25b1 - b1 = 120
q = 5
b1 = 5
b2 = b1q = 25
b3 = b2q = 125
Ответ: 155 = 5 + 25 + 125.