Insert the four arithmetic mean between 7 and -13, that 7 __, __, __, __, -13

7, 7+d, 7+2d, 7+3d, 7+4d, -13

so 7 + 5d = -13
5d = -20
d = -4

your sequence is:
7, 3, -1, -5, -9, -13