已知数列{an}的前n项和Sn=n2+2n,设数列{bn}满足an=log2bn,(1)求数列{an}的通项公式;(2)求数列{bn}

2025-06-27 19:24:18
推荐回答(1个)
回答1:

(1)∵Sn=n2+2n
∴当n≥2时,an=Sn-Sn-1=2n+1;
当n=1时,a1=S1=3,也满足上式,
∴综上得an=2n+1
(2)由an=log2bnbn2an22n+1

bn+1
bn
22n+3
22n+1
=4,
∴数列{bn}是等比数列,其中b1=8,q=4
Tn23+25++22n+1
8(1?4n)
1?4
8
3
(4n?1)