Let these three numbers be x, y and z respectively.

From the first condition: x+y+z=30, x, y, z becomes AP (arithmetic progression).

There is also an arithmetic average: x+z=2y.

So y= 10, x+z=20, and x=20-z from here.

From the second condition: x-5, y-4, z to GP (geometric series)

That is, 20-z-5, 10-4, and z becomes GP.

From the proportional term of z (15-z) = 6 2, we can get z 1=3 and z2= 12.

After examination, z 1 and z2 all meet the meaning of the question.

So these three numbers are: ① 17, 10,328,10, 12.