已知AN中,a1=2,6Sn=(an+1)(an+2),求数列An的通项公式An和Sn

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已知AN中,a1=2,6Sn=(an+1)(an+2),求数列An的通项公式An和Sn
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已知AN中,a1=2,6Sn=(an+1)(an+2),求数列An的通项公式An和Sn
已知AN中,a1=2,6Sn=(an+1)(an+2),求数列An的通项公式An和Sn

已知AN中,a1=2,6Sn=(an+1)(an+2),求数列An的通项公式An和Sn
6Sn=(an+1)(an+2)
6Sn-1=(an-1+1)(an-1+2),
相减得:6an=(an+an-1)(an-an-1)+3(an-an-1)
继续化简:(an+an-1)(an-an-1-3)=0 ④
是不是少了条件,an应该是正数吧?
④中:(an+an-1)不可能为0,所以:(an-an-1-3)=0
所以::an-an-1=d=3
所以an=a1+(n-1)d=3n-1
Sn=n(a1+an)/2
=(3n^2+n)/2