等差数列基础问题若{An}共有2n项,则Sn=n(An+An-1) 这个式子对么?我觉得是Sn=n(An+An+1)S为和,n是项数..怎么推出来的?S2n=n(An+An-1)是S2n

等差数列{An}.则S2n=n(An+A（n-1)）还是n(An+A(n+1))
S2n=2n(A1+A2n)/2=n(A1+A2n)=n(An+A(n+1))
或S2n=2n(A1+(2n-1)d/2)=n(2A1+(n-1)d))=n(An+A(n+1))

S2n=2n(A1+A2n)/2=n(An+An+1)
理由：A1+A2n=A1+A1+（2n-1)d=2A1+(2n-1)d
An+An+1=A1+(n-1)d+A1+nd=2A1+(2n-1)d