等差数列的性质{a(n)}为等差数列,公差为d,则Sn,S2n-Sn,S3n-S2n,也为等差数列,其公差为多少?_数学解答

等差数列的性质
{a(n)}为等差数列,公差为d,则Sn,S2n-Sn,S3n-S2n,也为等差数列,其公差为多少?

人气：427 ℃　时间：2020-06-20 17:25:26

解答

a(n)=a+(n-1)d,S(n)=na+n(n-1)d/2,S(2n)=2na+2n(2n-1)d/2,S(3n)=3na+3n(3n-1)d/2.S(3n)-S(2n)=na+nd[9n-3-4n+2]/2=na+nd[5n-1]/2,S(2n)-S(n)=na+dn[4n-2-n+1]/2=na+nd[3n-1]/2,[S(3n)-S(2n)]-[S(2n)-S(n)]=nd[2n]/2=...