设数列{An}的前n项和为Sn若An+1=3Sn,a1=1则An=

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an+1=3Sn
an=3Sn-1
an=Sn-Sn-1=an+1/饥答键3-an/烂巧举源3
2an/3=an+1/3
q=an+1/an=2
a1=1
an=a12^(n-1)=2^(n-1)

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a(n+1)=3Sn
S(n+1)-Sn=3Sn
S(n+1)=4Sn
{Sn}为等巧备宴比孝银数滚衫列
Sn=S1*q^(n-1)=1*4^(n-1)
an=Sn-S(n-1)=3*4^(n-2)

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