已知数列{an}满足a1=1,an+1=3an+3n,求an.
问题描述:
已知数列{an}满足a1=1,an+1=3an+3n,求an.
答
∵an+1=3an+3n,
∴
-an+1 3n+1
=an 3n
,1 3
∴数列{
}是以an 3n
为首项,1 3
为公差的等差数列,1 3
∴
=an 3n
+1 3
(n-1)=1 3
n,1 3
∴an=n•3n-1.