数列{an}满足:a1+3a2+5a3+…+(2n-1)•an=(n-1)•3n+1+3(n∈N*),则数列{an}的通
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数列{an}满足:a1+3a2+5a3+…+(2n-1)•an=(n-1)•3n+1+3(n∈N*),则数列{an}的通项公式为an=______.
∵a1+3a2+5a3+…+(2n-1)•an=(n-1)•3n+1+3,①
∴a1+3a2+5a3+…+(2n-3)•an-1=(n-2)•3n+3,
①-②,得:
(2n-1)an=(3n-3-n+2)•3n=(2n-1)•3n,
∴an=3n.
故答案为:3n.
∴a1+3a2+5a3+…+(2n-3)•an-1=(n-2)•3n+3,
①-②,得:
(2n-1)an=(3n-3-n+2)•3n=(2n-1)•3n,
∴an=3n.
故答案为:3n.
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