已知Sn是等差数列an的前n项和,bn=Sn⼀n

求证:数列bn是等差数列若S7=7,S15=75,求数列bn的前n项和Tn
2025-06-27 17:55:25
推荐回答(1个)
回答1:

an =a1+(n-1)d
Sn = [2a1+(n-1)d]n/2
bn = Sn/n
=[2a1+(n-1)d]/2
=a1 +(n-1)(d/2)
{bn}是等差数列, b1=a1, 公差=d/2

S7=7
a1+3d =1 (1)

S15=75
a1+7d= 5 (2)
(2)-(1)
d=1
from (1) , a1=-2
an = -2+(n-1)= n-3

Sn = (n-5)n/2
bn = Sn/n = (n-5)/2
Tn =b1+b2+...+bn
= (n-11)n/4