记等差数列{an}的前n项和为Sn,设S3=12,且2a1,a2,a3+1成等比数列,求Sn.

问题描述:

记等差数列{an}的前n项和为Sn,设S3=12,且2a1,a2,a3+1成等比数列,求Sn

设等差数列{an}的公差为d,由题意得

a22=2a1(a3+1)
3a1+
3×2
2
d=12
,解得
a1=1
d=3
a1=8
d=−4

∴sn=
1
2
n(3n-1)或sn=2n(5-n).