已知等差数列{an}满足：a3=7,a5+a7=26.

分类: 作业答案 • 2022-02-03 16:03:02

问题描述：

已知等差数列{an}满足：a3=7,a5+a7=26.
⑵令Tn=S1+S2+…+Sn(nεN^+)求T10.

答

=>a1=3,d=2 ==>Sn=n^2+2n
=>Tn=(1*1+2*2+3*3+...+n*n)+(2+4+6+...+2n)
=>Tn+Tn=(1*1+2+n*n)*n+(2+4+6+...+2n)
==>Tn=[n(1+n)^2+n*n+n]/2
带入n=10 ==>T10=660