设数列{an}是公比为正数的等比数列,a1=2,a3-a2=12.(1)求数列{an}的通项公式;(2)若数列{bn}满足:

2025-06-28 19:08:15
推荐回答(1个)
回答1:

(1)设数列{an}的公比为q,由a1=2,a3-a2=12,
得2q2-2q-12=0,即q2-q-6=0.
解得q=3或q=-2,
∵q>0,∴q=-2不合题意舍去,
an=2×3n?1
(2)由bn=log3(

3n
2
)+log3an,且an=2×3n?1,得
bn=log3(
3n
2
×2×3n?1)=log332n?1=2n?1

∴数列{bn}是首项b1=1,公差d=2的等差数列,
∴Sn=(a1+a2+…+an)+(b1+b2+…+bn)=
2(3n?1)
3?1
+
n(1+2n?1)
2
=3n-1+n2