In a geometric progression, the sum of the first second term is 60, and the sum

In a geometric progression, the sum of the first second term is 60, and the sum of the second and third terms is 180. Find the sum of the first five terms of this progression.

By condition:

b1 + b2 = 60.

b2 + b3 = 180.

Then:

b1 + b1 * q = 60.

b1 * (1 + q) = 60. (1)

b1 * q + b1 * q ^ 2 = 180.

b1 * q * (1 + q) = 180. (2)

Let us solve the system of two equations 1 and 2 for which equation 2 is divided into equation 1.

b1 * q * (1 + q) / b1 * (1 + q) = 180/60.

q = 3.

Then b1 = 60 / (1 + 3) = 15.

b5 = b1 * q ^ 4 = 15 * 81 = 1215.

Let’s determine the sum of the first five members.

Sn = (bn * q – b1) / (q – 1).

S5 = (1215 * 3 – 15) / (3 – 1) = 3630/2 = 1815.

Answer: The sum of the first five members is 1815.