The first term of the geometric progression (bn) is 4 and the denominator is 2, find the sum

The first term of the geometric progression (bn) is 4 and the denominator is 2, find the sum of the first eight terms of this progression.

A geometric progression is given, the first term of which is b1 = 4, and the denominator is q = 2. It is required to calculate the sum of the first eight terms of this progression (S8).

The sum of the first n terms of the geometric progression (Sn) is determined by the formula:

Sn = (b1 * (q ^ n – 1)) / (q – 1), where n is the number of summed members of the progression.

Let’s calculate the sum of the first eight terms of a given geometric progression:

S8 = (b1 * (q ^ 8 – 1)) / (q – 1);

S8 = (4 * (2 ^ 8 – 1)) / (2 – 1);

S8 = (4 * (256 – 1)) / 1;

S8 = 4 * 255;

S8 = 1020.

Answer: 1020.