已知等差数列[An],Sn=[（An+1）/2]^2,求An的通项公式n为下标,求救啊!

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已知等差数列[An],Sn=[（An+1）/2]^2,求An的通项公式n为下标,求救啊!
已知等差数列[An],Sn=[（An+1）/2]^2,求An的通项公式
n为下标,求救啊!

已知等差数列[An],Sn=[（An+1）/2]^2,求An的通项公式n为下标,求救啊!
因为Sn=[（an+1）/2]^2
所以S（n-1）=[（a(n-1)+1）/2]^2
两式相减得4an=(an+1)^2-(a(n-1)+1)^2
化简得(a(n-1)+1)^2=（an-1)^2
所以a(n-1)+1=an-1
所以an=a(n-1)+2
因为S1=[（a1+1）/2]^2
所以a1=1
所以an=a1+2(n-1)=2n-1

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