Sn=(d/2)*n^2+(a1-d/2)n是怎么推导出来的

Question

Sn=(d/2)*n^2+(a1-d/2)n是怎么推导出来的

Answer 1

把等差数列前n项和公式Sn=na1+dn(n-1)/2后半部分展开与前半部分合并:
Sn=na1+dn(n-1)/2=na1+(d/2)(n^2-n)
=na1+(d/2)n^2-(d/2)n
=(d/2)*n^2+(a1-d/2)n.