数列a1=-1,an+1=2an+4{3}^{n-1}a1=-1,an+1=2an+4{3}^{n-1},求an

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数列a1=-1,an+1=2an+4*{3}^{n-1}a1=-1,an+1=2an+4*{3}^{n-1},求an
数列a1=-1,an+1=2an+4*{3}^{n-1}
a1=-1,an+1=2an+4*{3}^{n-1},求an

数列a1=-1,an+1=2an+4*{3}^{n-1}a1=-1,an+1=2an+4*{3}^{n-1},求an
a(n+1)=2an+4×3^(n-1)
设a(n+1)-m3^n=2[an-m3^(n-1)]
∴a(n+1)=2an+m3^(n-1)
∴m=4
∴a(n+1)-4×3^n=2[an-4×3^(n-1)]
∴﹛an-4×3^(n-1)﹜是等比数列
∴an-4×3^(n-1)=(a1-4×3º)×2^(n-1)=-5×2^(n-1)
an=4×3^(n-1)-5×2^(n-1)
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a(n+1)=2an+4*3^(n-1)
a(n+1)/2^(n+1) - an/2^n = (3/2)^(n-1)
an/2^n -a1/2^1 = (3/2)^1+ (3/2)^2+..(3/2)^(n-1)
= 2(3/2)( (3/2)^(n-1) -1 )
= 2. (3/2)^n - 2
an/2^n = 2. (3/2)^n - 5/2
an = 2^n [2. (3/2)^n - 5/2 ]

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