The third term of the progression is equal to 8, the seventh is equal to -4 what is the difference of this progression.

Suppose that the first term of the given progression is equal to x, and the difference of the progression is equal to y.

Then, by the condition of the problem, the third term of the progression is equal to:

x + 2 * y = 8,

and the seventh member of the progression is:

x + 6 * y = -4.

From the first equation we express x:

x = 8 – 2 * y and substitute this value into the second equation:

8 – 2 * y + 6 * y = -4,

4 * y = – 4 – 8,

4 * y = -12,

y = -12: 4,

y = -3.

Answer: the difference in the progression is -3.