In a geometric progression, the sum of the first and second terms is 48

In a geometric progression, the sum of the first and second terms is 48, and the sum of the second and third terms is 144. Find the first three terms of this progression.

According to the condition of the problem, a geometric progression bn is given.
Let’s use the formula for the nth term of the geometric progression bn = b1 * q ^ (n-1), where b1 is the first term of the geometric progression, q is the denominator of the geometric progression.
It is known that the sum of the first and second terms of this geometric progression is 48, therefore, the following ratio is true:
b1 + b1 * q = 48.
Also, according to the condition of the problem, the sum of the second and third members of this geometric progression is equal to 144, therefore, the following ratio is true:
b1 * q + b1 * q ^ 2 = 144,
or
q * (b1 + b1 * q) = 144.
We solve the resulting system of equations. Substituting into the second equation the value b1 + b1 * q = 48 from the first equation, we get:
q * 48 = 144;
q = 144/48;
q = 3.
Knowing q, we find b1:
b1 + b1 * 3 = 48;
b1 * 4 = 48;
b1 = 48/4;
b1 = 12.
Find b2 and b3:
b2 = b1 * q = 12 * 3 = 36;
b3 = b2 * q = 36 * 3 = 108.

Answer: the first term of this geometric progression is 12, the second term is 36, the third term is 108.