数列是初等数学的重要内容之一。处理这类问题的有效方法是归纳法,但对于某些结构较复杂的数列。却未必是万宝灵丹。本文介绍求数列通项的另一种方法,它着重于探索数列通项的形式,在此基础上利用待定系数的方法求其通项。一、满足一阶递归关系式α_n=pα_(n-1)+r的数列的通项α_(no)其中p、r是常数p≠0(p=0是常数列)。 (1)若p=1,则α_n-α_(n-1)=r,{α}是等差数列,∴α_n=c_1+c_2,其中c_1=r。 (ii)若p≠1。则令c_1=r/1-p The series is one of the important contents of elementary mathematics. An effective way to deal with this type of problem is induction, but for some structures with more complex sequences. It may not be a Wanbao panacea. This paper introduces another method for obtaining general terms of numbers. It focuses on exploring the form of general terms and uses the method of undetermined coefficients to find its general terms. 1. The general term α_(no) of a sequence satisfying the first-order recursive relation α_n=pα_(n−1)+r, where p and r are constants p≠0 (p=0 is a constant column). (1) If p=1, then α_n-α_(n-1)=r, {α} is an arithmetic progression, ∴α_n=c_1+c_2, where c_1=r. (ii) If p≠1. Then let c_1=r/1-p