Find the sum of the first five terms of the geometric progression given by the formula: An = -3n + 2.

Apparently, there is a typo in the condition, since the formula for the n-th term, which we see in this problem, sets an arithmetic progression.

So, the arithmetic progression (an) is given by the formula of the nth term of the progression an = -3n + 2.

In order to find the sum of the first five members of an arithmetic progression, recall the formula:

Sn = (a1 + an) / 2 * n;

S5 = (a1 + a5) / 2 * 5;

Let’s find the first and fifth term of the progression.

a1 = -3 * 1 + 2 = -3 + 2 = -1;

a5 = -3 * 5 + 2 = -15 + 2 = -13.

Let’s apply the formula and get:

S5 = (a1 + a5) / 2 * 5 = (-1 – 13) / 2 * 5 = -14/2 * 5 = -7 * 5 = -35.