已知等差数列｛an｝满足：a3=7,a5+a7=26.｛an｝的前n项和为Sn1.求An及Sn；2.令Bn=1/An^2-1(n∈N*),求数列｛bn｝的前n项和Tn

Question

已知等差数列｛an｝满足：a3=7,a5+a7=26.｛an｝的前n项和为Sn 1.求An及Sn；2.令Bn=1/An^2-1(n∈N*),求数列｛bn｝的前n项和Tn

Answer 1

a3=a1+2d=7,
a5+a7=2a6=2(a1+5d)=26
a1=3
d=2
an=a1+(n-1)d=3+2(n-1)=2n+1
Sn=(3+2n+1)n/2=n(n+2)
Bn=1/An^2-1=1/4n(n+1)
Tn=1/4(1/1-1/2+1/2-1/3+...+1/n -1/(n+1))
=1/4(1-1/(n+1))
=n/4(n+1)