Let $S_n$ denote the sum of $n$ terms of an A.P. whose first term is $a$. If the common difference $d$ is given by $d=S_n-k{S}_{n-1}+S_{n-2}$, then $k=$

The first and last terms of an A.P. are $a$ and $l$ respectively. If $S$ is the sum of all the terms of the A.P. and the common difference is given by $\frac{l^2-a^2}{k-(l+a)}$, then $k=$