已知等差数列【an】满足:a3=7,a5+a7=26.【an】的前n项和为Sn.(1)求a4及Sn;

题目

已知等差数列【an】满足:a3=7,a5+a7=26.【an】的前n项和为Sn.(1)求a4及Sn;
(2)bn=1/(an^2-1)(n属于N*),求数列【bn】的前n项和Tn

答案

a5=a3+2d,a7=a3+4d
a5+a7=2a3+6d
26=2*7+6d
d=2
a4=a3+d=7+2=9
a1=a3-2d=7-2*2=3
Sn=na1+n(n-1)d/2=n^2+2n
an=a1+nd=3+2n
bn=1/(an^2-1)=1/[4(n+2)(n+1)]=1/4[(1/(n+1)-1/(n+2)]