Need help in SPP

What are we supposed to keep in the F1 vector for SPP problem?

S(n) = S(n-1) + a(n), we have S(n-1) and other k terms on which a(n) depends, we replace them by the first k values for a(i). But what should we place in S(n-1) position in F1 matrix? Sum of first k elements or sum of first element? or something else?
Thanks.