Find the difference of the arithmetic progression if its fifth term is -1, and the eleventh term is -5.

Let’s denote the number that is in the first place in this sequence through c1, and the difference of the arithmetic progression through d.

In the initial data for this task, it is reported that in this sequence, the number -1 is at the 5th position, and the number -5 at the 11th position, therefore, the following relations take place:

c1 + (5 – 1) * d = -1;

c1 + (11 – 1) * d = -5.

We solve the resulting system of equations.

Subtracting the first equation from the second, we get:

c1 + (11 – 1) * d – c1 – (5 – 1) * d = -5 – (-1);

10d – 4d = -5 + 1;

6d = -4;

d = -4/6 = -2/3.

Answer: the difference of the arithmetic progression is -2/3.