求递推数列的通项公式是高中数学教学中的一个长期被关注的热点问题,因为它不仅能让学生领会数学的化归思想和方法,强化对基础知识、基本技能的理解和掌握,特别是对等差数列、等比数列的定义和前n项和公式的本质的内涵和外延的认识,而且能有效地培养学生观察能力、发散思维能力。本文根据教学实践对an+an+1=f(n)(n∈N+)“型递推数列的通项公式进行探讨,并根据f(n)的特点给出几种常用方法: The general formula for seeking recursion series is a hot issue of long-term concern in high school mathematics teaching because it not only enables students to comprehend the idea and method of returning math to mathematics, but also strengthens the understanding and mastery of basic knowledge and basic skills, especially It is the definition of the sequence of equal difference, the definition of geometric series, the connotation and extension of the essence of the first n terms and formulas, and can effectively cultivate students’ observation ability and divergent thinking ability. According to the teaching practice, this article discusses the general formula of an + an + 1 = f (n) (n∈N +) ”recursion series, and gives some common methods according to the characteristics of f (n)