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
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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
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
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
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+2n
a(n+1)+n+1=3an+2n+n+1=3(an+n)+1
令bn=an+n
则b(n+1)=3bn+1
b(n+1)+1/2=3bn+1+1/2=3(bn+1/2)
所以{bn+1/2}是等比数列
故bn+1/2=(b1+1/2)*3^(n-1)=(a1+1+1/2)*3^(n-1)=(7/2)*3^(n-1)
所以bn=(7/2)*3^(n-1)-1/2
故an=bn-n=(7/2)*3^(n-1)-1/2-n
a(n+1)=3an+2^(n-1)
a(n+1)+2*2^(n-1)=3an+2^(n-1)+2*2^(n-1)
a(n+1)+2^n=3an+3*2^(n-1)
a(n+1)+2^n=3【an+2^(n-1)】 (n>=2)
a2=3a1+1=7
所以{a(n+1)+2^n}是一个以7为首项,3为公比的等比数列,
an+2^(n-1)=7*3^(n-1)
an=7*3^(n-1)-2^(n-1)