Question

一道高中数列题,..已知正项等差数列{an}的前n项和为Sn,若S3=12,且2a1,a2,a3+1成等比数列.求｛an

Answer 1

1.

设an=a1+(n-1)d,a1＞0，d＞0

Sn=na1+n(n-1)d/2

S3=3a1+3d=12,a1+d=4

(2a1)(a3+1)=(a2)^2,

(2a1)(a1+2d+1)=(a1+d)^2,

a1(d+5)=8

(4-d)(d+5)=8

d^2+d-12=0

d=3

a1=1

an=1+...