The general form of diff equation for an LTi system is :
$ y(n) = - \sum_{k=1}^N a_k \cdot y(n-k) + \sum_{k=0}^M b_k \cdot x(n-k) $
My questions are:
1) why is the first term negative ?
2) why limits of $k$ are from $1$ to $N$ and not $0$ to $N$ ?
3) what does $M$ represent if $N$ represents the order of the system ?