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

∵an+1=3an+3n

an+1
3n+1
-
an
3n
=
1
3

∴数列{
an
3n
}是以
1
3
为首项,
1
3
为公差的等差数列,
an
3n
=
1
3
+
1
3
(n-1)=
1
3
n,
∴an=n•3n-1