Because the first three numbers are arithmetic progression.

There is 2b=a+c, so a = 2b-c.

The last three become geometric series, c*c=b*d, so d = c * c/b.

a+d=37

So 2b-c+c*c/b=37.

b+c=36

So we can calculate b= 16, c=20 or b=8 1/4, and c=63/4.

When b= 16 and c=20, solve a = 12 and d = 25.

When b=8 1/4 and c=63/4, solve a=99/4 and d=49/4.

So the number of 4 is 12, 16, 20, 25 or 99/4, 8 1/4, 63/4, 49/4.