Sequences

From arithmetic and geometric sequences to the $\Sigma$ notation

Overview

A sequence is an ordered list of numbers following a rule. In high school, one learns formulas for arithmetic and geometric sequences and how to compute sums using the $\Sigma$ notation; in university, these ideas extend to convergence and divergence.

$a_1$

$a_2$

$a_3$

$\cdots$

$a_n$

$\cdots$

Figure 1: A sequence $\{a_n\}$ — an ordered list of numbers following a rule.

Table of Contents by Level

Introduction

Arithmetic sequences, geometric sequences, $\Sigma$ notation and formulas. High school level.

Main Topics

Arithmetic sequence: a sequence in which the difference between consecutive terms is constant.
Geometric sequence: a sequence in which the ratio between consecutive terms is constant.
$\Sigma$ notation: a symbol for sums, with its basic formulas.
Recurrence relation: an equation that defines a sequence inductively.