Find the sum of the first eight terms of the arithmetic progression, the first term which is – 12, and the second – 9

We have an arithmetic progression for which the first two terms are known:

a1 = -12;

a2 = -9.

Find the sum of the first eight terms of the arithmetic progression.

Let’s write the formula for the nth term of the arithmetic progression:

an = a1 + d * (n – 1);

Now let’s write this formula for the second term of the progression:

a2 = a1 + d;

Subtract from the value of the second term the value of the first:

a2 – a1 = d.

d = -9 – (-12) = 3.

Now let’s find the value of the eighth term of the progression:

a8 = a1 + 7 * d;

a8 = -12 + 7 * 3;

a8 = 9.

Then:

S8 = (a1 + a8) * 8/2;

S8 = 4 * (-12 + 9);

S8 = -12.