设数列an满足a1=2,a(n+1)=3an+2^(n-1),求an2,设数列an满足a1=2,a(n+1)=3an+2n,求an_数学解答

设数列an满足a1=2,a(n+1)=3an+2^(n-1),求an
2,设数列an满足a1=2,a(n+1)=3an+2n,求an

人气：382 ℃　时间：2019-11-17 05:59:20

解答

1.a(n+1)=3an+2^(n-1)a(n+1)+2^n=3an+2^(n-1)+2^n=3[an+2^(n-1)]所以数列{an+2^(n-1)}是等比数列故an+2^(n-1)=[a1+2^(1-1)]*3^(n-1)=3^n所以an=3^n-2^(n-1)2.a(n+1)=3an+2na(n+1)+n+1=3an+2n+n+1=3(an+n)+1令bn=an+n...