For any sequence of numbers A = (a1, a2, a3, …), define ΔA to be the sequence (a2- a1, a3 – a2, a4 – a3,…) whose nth term is an+1 – an. Suppose Δ2A = (1,1,1,1,...) and a19 = 0 = a92. Find a1.
If anyone can help or provide any information that would be great. I have no clue where to start. I think finite calculus makes this significantly easier.