19.一直数列An,A1=m,A(n+1)=2An+3^(n+1).
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19.一直数列An,A1=m,A(n+1)=2An+3^(n+1).
(1)设Bn=A(n+1)/3^n,求Bn通项公式.
(1)设Bn=A(n+1)/3^n,求Bn通项公式.
A(n+1)=2An+(3-2)*3^(n+1),A(n+1)-3^(n+2)=2(An-3^(n+1)),
令Cn=An-3^(n+1),则C1=m-9,Cn=(m-9)*2^(n-1).
故An=(m-9)*2^(n-1)+3^(n+1).于是Bn=(m-9)*(2/3)^n+9.
令Cn=An-3^(n+1),则C1=m-9,Cn=(m-9)*2^(n-1).
故An=(m-9)*2^(n-1)+3^(n+1).于是Bn=(m-9)*(2/3)^n+9.
19.一直数列An,A1=m,A(n+1)=2An+3^(n+1).
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