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.
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