In the arithmetic progression (An) it is known that a5 = -132, a9 = -256. Find the difference of the arithmetic progression

Let’s use the formula of the nth term of the arithmetic progression an = a1 + (n – 1) * d, where a1 is the first term of the arithmetic progression, d is the difference of the arithmetic progression.

By the condition of the problem, the fifth term a5 of this arithmetic sequence is -132, and the ninth term a9 of this sequence is -256.

Substituting these values, as well as the values ​​n = 5 and n = 9 in the formula for the nth term of the arithmetic progression, we get:

a1 + (5 – 1) * d = -132;

a1 + (9 – 1) * d = -256.

Subtracting the first equation from the second, we get:

a1 + 8 * d – a1 – 4 * d = -256 – (-132);

4 * d = -124;

d = -124 / 4;

d = -31.

Answer: the difference of this arithmetic progression is -31.