Sn为数列{an}的前n项和,已知an>0,且an^2+an=4Sn+3。求an通项公式。

2025-01-21 05:58:57
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回答1:

4Sn=an^2+2an-3 4S1=a1^2+2a1-3 a1=1
4Sn-1=an-1^2+2an-1-3
4an=an^2-an-1^2+2an-2an-1
an^2-an-1^2-2an-2an-1=0
(an+an-1)(an-an-1-2)=0
an=an-1+2 an=1+(n-1)*2=2n-1