Question 1039330
To add 5 arithmetic means to 1, , , , , , 7 is simple, for the fact that there are 6 'differences', and the total difference is 6. So we get, 1,2,3,4,5,6,7.

To get from x to -5x is the same, it's 6 differences of x, -x to be clear. The same for 3y to 9y, it's just a difference of y. 

(x+3y) (0x+4y)(-1x+5y)(-2x+6y)(-3x+7y)(-4x+8y) (-5x+9y)