已知数列an,a1=2,且a(n+1)=2an+3n,求an

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已知数列an,a1=2,且a(n+1)=2an+3n,求an已知数列an,a1=2,且a(n+1)=2an+3n,求an已知数列an,a1=2,且a(n+1)=2an+3n,求an因为a(n+1)=2

已知数列an,a1=2,且a(n+1)=2an+3n,求an
已知数列an,a1=2,且a(n+1)=2an+3n,求an

已知数列an,a1=2,且a(n+1)=2an+3n,求an
因为a(n+1)=2an+3n
令a(n+1)+x(n+1)+y=2[an+xn+y]
则a(n+1)=2an+xn+y-x
所以x=3,y-x=0故x=3,y=3
所以a(n+1)+3(n+1)+3=2[an+3n+3]
所以数列{an+3n+3}是等比数列,首项是a1+3+3=8,公比是q=2
所以an+3n+3=8*2^(n-1)=2^(n+2)
所以an=2^(n+2)-3n-3