一类递推数列通项公式求解的普适性方法

Generally Applicable Method for General Term Formula of a Recurrence Sequence

摘要: 求递推数列通项公式在高考及各类数学竞赛中既是重点又是难点，求通项公式的方法多、技巧强，利用等差、等比数列公式很难直接求得结果。导致学生畏惧，不能准确求解。因此探讨求递推数列通项公式的解题技巧和方法非常必要。基于此，利用同构转换思想，系统探讨了求解一类递推数列通项公式普遍适用的方法，该方法思想可操作性强，既简单又易掌握。

Abstract: It is not only the key but also the difficult point to find the general term formula of the recursive sequence in the college entrance examination and all kinds of mathematics competitions. Many methods for solving the formula of the general term are presented, and its technique is strong. It is difficult to obtain the result directly by using arithmetic sequence and geometrical sequences. As a result, students are afraid and cannot accurately solve the problem. Therefore, it is very necessary to explore the technique and method of solving the general term formula of recursive sequence. Based on this, using the idea of isomorphic transformation, this paper systematically discusses the general method of solving the general term formula of a kind of recursive sequence, which has strong operability and is simple and easy to master.