定理:在等差数列{a_n}中,若m+n=p+q(m,n,p,p,q∈N),则a_m+a_n=a_p+a_q. 等差数列这个性质从论证、理解到应用都易被学生接受,本文试图剖析定理的内涵并通过一些例子就常规方法与定理另解或巧解的对照,增强应用定理的能力,达到在相关问题中巧用定理变繁为简,化腐朽为神奇的功效. (1)源于课本:课本是学生学习知识,提高技能,掌握数学思想方法,形成良好个性品质的第一手材料.教科书虽没有将定理作为等差数列的性质列出,但教材中两处折射出这个定理举足轻重的地位.其一是倒序相加法推导等差 Theorem: In the arithmetic sequence {a_n}, if m+n=p+q(m,n,p,p,q∈N), then a_m+a_n=a_p+a_q. The property of the arithmetic progression is from the argument, Understand that the application is easily accepted by students. This article attempts to analyze the connotation of the theorem and compares the conventional method with the theorem through some examples. It enhances the application theorem’s ability to achieve simple and complicated theorem in related problems. (1) Originated from textbooks: Textbooks are first-hand materials for students to learn knowledge, improve their skills, master mathematics ideas and methods, and form good personality qualities. Although textbooks do not use the theorem as the property of arithmetic sequences Listed, but reflected in two places in the textbook, this theorem plays a decisive role. The first is the reverse order addition method to derive the difference