数列an满足a1=1,an+1=3an+3^n+1,求an的通项an数列an满足a1=1,a（n+1）=3an+3^（n+1）,求an的通项an,求数列an的前n项和

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数列an满足a1=1,an+1=3an+3^n+1,求an的通项an数列an满足a1=1,a（n+1）=3an+3^（n+1）,求an的通项an,求数列an的前n项和
数列an满足a1=1,an+1=3an+3^n+1,求an的通项an
数列an满足a1=1,a（n+1）=3an+3^（n+1）,求an的通项an,求数列an的前n项和

数列an满足a1=1,an+1=3an+3^n+1,求an的通项an数列an满足a1=1,a（n+1）=3an+3^（n+1）,求an的通项an,求数列an的前n项和
下面这个方法较简单：
a(n+1)=3an+3^(n+1),两边同除以3^(n+1)可得：
a(n+1)/ 3^(n+1)= 3an/ 3^(n+1)+1,
a(n+1)/ 3^(n+1)= an/ 3^n+1,
设an/ 3^n=bn,则b(n+1)=bn+1,
这说明数列{bn}是公差为1的等差数列,首项为b1=a1/3=1.
bn=b1+(n-1)•1=1+(n-1)•1=n.
即an/ 3^n=n,
∴an=n•3^n.
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