递归数列也称为递归函数,最早出现于数论.本世纪以来,新兴的数学基础和数理逻辑以递归函数为重要研究对象,此外在计算理论、概率论、组合数学和量子力学等学科,递归函数也有多种应用. 本文讨论用变换的方法,把各种初等递归数列转化为等差和等比数列,从而求得其通项公式.交换是数学中有广泛应用的重要技巧,在中学中适当加强变换技巧的训炼,是有助于沟通初等数学和高等数学的教学 Recursive sequence is also called recursive function. It first appeared in number theory. Since the beginning of this century, the emerging mathematics foundation and mathematical logic have taken recursive function as the important research object. In addition, recursive functions have been used in computational theory, probability theory, combinatorial mathematics and quantum mechanics. There are also many applications. This paper discusses the use of transformation methods to convert various elementary recursive sequences into arithmetic and geometric sequences to obtain their general term formulas. Exchange is an important technique widely used in mathematics and is appropriate in middle schools. Strengthen the training of transforming skills is helpful to communicate the teaching of elementary mathematics and advanced mathematics