Given an arithmetic progression, calculate the sum of 9 terms if a13 = 2 d = 1.

We are given an arithmetic progression by the formula (an) by its thirteenth term and the difference of the arithmetic progression a13 = 2, d = 1.

In order to find the sum of the first 9 terms of an arithmetic progression, we need to find the first term of this progression.

Let’s remember the formula for finding the n-th term of the progression.

an = a1 + d (n – 1);

a13 = a1 + 12d;

2 = a1 + 12 * 1;

a1 = 2 – 12;

a1 = -10.

Let’s remember the formula for finding the sum:

Sn = (2a1 + (n – 1) d) / 2 * n;

S9 = (2a1 + (9 – 1) d) / 2 * 9 = (2 * (-10) + 8 * 1) / 2 * 9 = (-20 + 8) / 2 * 9 = -12/2 * 9 = -6 * 9 = -54.