记等差数列an的前n项和为Sn,设S3=12,且2a1a2a3+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2a1a2a3+1成等比数列,求Sn
答
{an}是等差数列S3=a1+a2+a3=3a2=12a2=4设公差为da1=4-d a3=4+d2a1,a2,a3+1成等比数列(a2)^2=2a1·(a3+1)4^2=2(4-d)(4+d+1)8=(4-d)(d+5)8=20-d-d^2d^2+d-12=0(d+4)(d-3)=0d=-4 或 d=3若d=-4,则a1=8,an=a1+d(n-1)=8-4(...