Sn=n^2+kn
Sn-1=-(n-1)^2+k(n-1)
an=Sn-Sn-1=-n^2+kn+(n-1)^2-k(n-1)=2n+k+1
limnan/Sn
=limn(2n+k+1)/(-n^2+kn)
=lim-(2n^2+nk+n)/(n^2-kn)
=lim-(2+k/n+1/n)/(1-k/n)
=-2
Sn=n^2+kn
Sn-1=-(n-1)^2+k(n-1)
an=Sn-Sn-1=-n^2+kn+(n-1)^2-k(n-1)=2n+k+1
limnan/Sn
=limn(2n+k+1)/(-n^2+kn)
=lim-(2n^2+nk+n)/(n^2-kn)
=lim-(2+k/n+1/n)/(1-k/n)
=-2