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数列{a_n},如果对于任意相邻的三项a_(k+2),a_(k+1),ak满足Aa_(k+2)+Ba_(k+1)+Ca_k=0(AC≠0,k=1,2,3,…),则称这数列为二阶递归数列。关于二阶递归数列通项公式虽然已有很多论述,但由于使用的是母函数法,这使很多中学生不容易接受,或者使用逐推法而把问题搞得相当繁琐。笔者在下面提供的一种方法是以现行中学数学教材为基础的、能被一般学生所接受的,因而可以作为中学生课外阅读材料。
The sequence {a_n}, if for any adjacent three terms a_(k+2), a_(k+1), ak satisfies Aa_(k+2)+Ba_(k+1)+Ca_k=0(AC≠0 ,k=1,2,3,...), then it is called a second-order recursive sequence. Although there have been many discussions about the second-order recursive sequence general term formula, since the mother function method is used, it is not easy for many middle school students to accept or use the push-by-push method to make the problem rather cumbersome. The method provided by the author below is based on the existing middle school mathematics textbooks and can be accepted by the average student, so it can be used as an extracurricular reading material for middle school students.