In a geometric progression, the sum of the first and second terms is 60, and the sum of the second and third shuttles is 84.

In a geometric progression, the sum of the first and second terms is 60, and the sum of the second and third shuttles is 84. Find the first three terms of this progression.

The sum of the first and second terms is exponentially 60
b1 + b1q = 60
the sum of the second and third terms is 84
b1q + b1q² = 84
Find the first three terms of this progression
b1, b2 = b1q, b3 = b1q² -?
b1 + b1q = 60
b1 * (1 + q) = 60
b1 = 60: (1 + q)

b1q + b1q² = 84
b1q * (1 + q) = 84
b1q = 84: (1 + q)

q = b2: b1 = b1q: b1 = (84: (1 + q)) 🙁 60: (1 + q)) = 84: 60 = 7/5

b1 = 60: (1 + q) = 60: (1 + 7/5) = 60: 12/5 = 60 * 5/12 = 25
b2 = b1q = 25 * 7/5 = 35
b3 = b1q² = 25 * (7/5) ² = 25 * 49/25 = 49
b1, b2, b3 – members of a geometric progression q – denominator of a geometric progression
b1 = 25 b2 = 35 b3 = 49