The Method for Finding the General Term Formula of a Class of Second-Order Non-Homogeneous Linear Recurrent Sequences

二阶非齐次线性递推数列是高中数学竞赛的重要内容，求解方法的方法有多种，例如特征方程法、生成函数法等，但是这类方法对于高中生来说有一定的难度，因此本文用类比的方法来进行求解，学生更容易理解，也能让学生体会数学的奥妙。Second-order non-homogeneous linear recurrent sequences are an important part of high school mathematics competitions. There are various methods for solving them, such as the characteristic equation method and the generating function method. However, these methods are somewhat difficult for high school students. Therefore, this paper uses the analogy method for solution, which makes it easier for students to understand and also enables them to appreciate the mysteries of mathematics.