已知等差数列{an}的前n项和为Sn,公差d≠0,且S3=9,a1,a3,a7成等比数列.(1)求数列{an}的通项公式;

2024-12-19 15:21:25
推荐回答(1个)
回答1:

(1)∵a1,a3,a7成等比数列.
∴a32=a1a7
即(a1+2d)2=a1(a1+6d),
化简得d=

1
2
a1,d=0(舍去).
∴S3=3a1+
3×2
2
×
1
2
a1
=
9
2
a1=9,得a1=2,d=1.
∴an=a1+(n-1)d=2+(n-1)=n+1,即an=n+1.
(2)∵bn=2an=2n+1,∴b1=4,
bn+1
bn
=2

∴{bn}是以4为首项,2为公比的等比数列,
∴Tn=
4(1?2n)
1?2
=2n+2-4.