The first term of the geometric progression b1 = 2 and the denominator q = -3 find the sum of the first

The first term of the geometric progression b1 = 2 and the denominator q = -3 find the sum of the first five members of the progression.

Given:

bn – geometric progression,

b1 = 2,

q = -3.

Find: S5.

Recall the formula for finding the sum of the first n terms of a geometric progression (Sn):

Sn = (b1 * (q ^ n – 1)) / (q – 1), where

b1 – the first member of the progression,

q is the denominator of the progression,

n is the number of summed members.

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

S5 = (2 * ((-3) ^ 5 – 1)) / (-3 – 1);

S5 = (2 * (-243 – 1)) / (-4);

S5 = (-244) / (-2);

S5 = 122.

Answer: S5 = 122.