R, 62 bytes
function(l)c(p<-Reduce(function(x,y)(x+y)/2,l),a<-mean(l),p-a)
Pretty straightforward implementation.
R, 51 bytes
function(l,L=sum(l|1))sum(l*2^(c(1,1:(L-1))-L)-l/L)
This approach is perhaps more amenable to an improvement that I have overlooked, but only returns the difference progressive - arithmetic.
Giuseppe
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