Lesson 2.1. Review of Sequence and Series

Learning Outcomes of the Lesson

At the end of the lesson, the studentis able to:

(1) Illustrate a series; and

(2) Differentiate a series from a sequence.

Lesson Outline

(1) Sequence and series

(2) Different types of a sequenceand series (Fibonacci sequence, arithmetic and geometriic sequence and series and harmonic series)

(3) Difference between sequence and series.

Introduction

In this lesson, we will review the definitions and different types of a sequenceand series.

Lesson Proper

A “sequence” (called a “progression” in British English) is an ordered list of numbers; the numbers in this ordered list are called the “elements” or the “terms” of the sequence.

A “series” is what you get when you add up all the terms of a sequence; the addition, and also the resulting value, are called the “sum” or the “summation”. For instance, “1, 2, 3, 4” is a sequence, with terms “1”, “2”, “3”, and “4”; the corresponding series is the sum “1 + 2 + 3 + 4”, and the value of the series is 10.