若数列{an}是公差为d,首项为a1的等差数列,则其前n项和公式为:S=na1+n(n-1)/2d. 变式一 Sn=d/2n2+(a1-d/2)n. 看到这一变式,同学们容易想到学过的二次函数f(x)=ax2+bx(a≠0),它的图像是一条抛物线.因此,等差数列中的前n项和Sn及项数n构成的有序数对(n,Sn)在同一条抛物线上,是该抛物线上的一群孤立的点. 变式二 Sn/n=d/2n+(a1-d/2). 看到这一变式,同学们应该容易想到学过 If the sequence {an} is an equal-difference sequence whose tolerance is d and the first item is a1, the first n terms and the formula is: S=na1+n(n-1)/2d. Variant-Sn=d/2n2+( A1-d/2)n. To see this variant, students easily think of the learned quadratic function f(x)=ax2+bx(a ≠ 0). Its image is a parabola. Therefore, the difference is The first n items in the sequence and the number of Sn and the number of items n (n, Sn) are on the same parabola and are a group of isolated points on the parabola. Variant II Sn/n=d/2n+(a1 -d/2). To see this variant, students should easily think of learning