Sum of Arithmetic Sequences: Formula & Applications | IGCSE数学：等差数列求和公式与应用

📚 Sum of Arithmetic Sequences: Formula & Applications | IGCSE数学：等差数列求和公式与应用

An arithmetic sequence is one of the most common number patterns in IGCSE Mathematics. This article explains the sum formula for arithmetic sequences, shows how it is derived, and applies it to a range of exam-style problems.

等差数列是 IGCSE 数学中最常见的数列之一。本文将讲解等差数列的求和公式，展示公式如何推导，并通过多种考试型问题加以应用。

1. What is an Arithmetic Sequence? | 什么是等差数列？

An arithmetic sequence, also called an arithmetic progression, is a sequence in which the difference between any two consecutive terms is constant. This constant difference is called the common difference, usually written as d.

等差数列（arithmetic sequence / arithmetic progression）是指任意两个相邻项之间的差保持不变的数列。这个常数称为公差，通常用 d 表示。

For example, 3, 7, 11, 15, … is arithmetic because each term is 4 more than the previous term. Here the first term is a = 3 and the common difference is d = 4.

例如，3，7，11，15，… 是等差数列，因为每一项都比前一项多 4。这里首项 a = 3，公差 d = 4。

Similarly, 20, 16, 12, 8, … is arithmetic with a = 20 and d = -4. Notice that the common difference can be negative when the sequence is decreasing.

同理，20，16，12，8，… 也是等差数列，其中 a = 20，d = -4。注意：当数列递减时，公差可以为负数。

2. Notation You Must Know | 必备符号与定义

Before using the sum formula, it is important to understand the standard notation used in Edexcel IGCSE Mathematics.

在使用求和公式之前，理解 Edexcel IGCSE 数学中的标准符号非常重要。