To be Christmassy, break it into a red sequence and a green sequence:

8,2,4,1,2,0.5,1,__

The red numbers go: 

8, take half, 4, take half, 2, take half, 1.

The green numbers go:

2, take half, 1, take half, 0.5, take half, __.

So half of 0.5 is 0.25.

Edwin