Question

设数列an为等差数列, S7=7, S15=75, bn=Sn / n，，

求{ bn }的前n项和Tn

Answer 1

S7=7(a1+a7)/2=7 a1+a7=2 2a1+6d=2 a1+3d=1
S15=15(a1+a15)/2=75 a1+a15=10 2a1+14d=10 a1+7d=5
d=1 a1=-2
Sn=n(-2-2+n-1)/2=n(n-5)/2
bn=Sn/n=(n-5)/2
b1=-2 d=1/2
Tn=n(-2+n/2-5/2)/2=n(n/4-9/4)