教材中对等差数列的概念、通项公式 a_n=a_1+(n-1)d,前 n 项和的公式 s_n=n(a_1+a_n)/2中的五个基本量 a_1,d,n,a_n,S_n,只要求“知三求二”.但在竞赛题中有一大类较特殊的数列求前 n 项之和用以上知识不易解决.本文先给出关于等差数列的一个重要定理,并给出完整的证 The concept of arithmetic progression in the textbook, the general formula a_n=a_1+(n-1)d, the formula of the first n terms s_n=n(a_1+a_n)/2, the five basic quantities a_1,d,n, A_n, S_n only require “knowing three and seeking two.” But in the contest title, there is a large class of more special numbers. The sum of the n terms is not easy to solve with the above knowledge. This article first gives an important theorem about arithmetic progression. And give a complete certificate