The first term of the geometric progression is 11 and the denominator of the progression is 2

The first term of the geometric progression is 11 and the denominator of the progression is 2, find the sum of the first five members of this progression.

The sum of the first n terms of the geometric progression Sn can be calculated by the formula:

Sn = (b1 * (q ^ n – 1)) / (q – 1),

where b1 is the first term of the progression, q is its denominator, n is the number of summed terms.

Let us find the sum of the first five terms (S5) of a given geometric progression, in which b1 = 11, q = 2:

S5 = (b1 * (q ^ 5 – 1)) / (q – 1);

S5 = (11 * (2 ^ 5 – 1)) / (2 – 1);

S5 = (11 * (32 – 1)) / 1;

S5 = 11 * 31;

S5 = 341.

Answer: the sum of the first five terms of a given geometric progression is 341.