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Topic Overview
Most people have met sequences at some stage in their lives. Questions of the form "what is the next number in the list 1, 4, 9, 16, …" frequently appear in quizzes. The list of numbers, separated by commas, is a sequence.
In practice, the numbers in the list usually follow some pattern. In the example above, the next number is 25, because it is the square of 5. So what is a series? A series is just what we get when we add some of the terms of a sequence, e.g., 1+4+9+16.
Like most ideas treated mathematically, we find that we have to introduce terminology and notation to allow us to develop fully the properties of series. Also, there are many different kinds of sequence and series. However, we only have to investigate two kinds on our course, namely arithmetic and geometric sequences and series.
Sequences and series are examined in Question 5 on Paper 1 each year. Like most other questions on the first paper, a certain proficiency with algebra is required to answer many of the harder questions on sequences and series. But the algebra content is usually nowhere near that required in algebra itself, functions and differentiation.
Topic Structure
The study of Senior Cycle Sequences and Series can be divided into the following sections:
Sequence and Series Notation
Arithmetic Sequences and Series
Geometric Sequences and Series
Links
http://cne.gmu.edu/modules/dau/algebra/series/gs_frm.html
The section of the site we link to here is entitled 'The Center for the New Engineer'. Don't be put off by the strange title, the page itself has a couple of interesting problems of a practical nature on geometric series.
http://www.geocities.com/CapeCanaveral/Launchpad/2426/index13.html
This link is to Chapter 13, on Sequences and Series. Much of the material in this chapter is relevant. There are many definitions, examples and exercises given.
http://learn.lboro.ac.uk/olmp/book.html
To use this site, which is hosted by Loughborough University in the UK, it will be necessary to scroll down and choose the link to 'Sequences and Series'. This will open a pdf document in Adobe Acrobat Reader. It contains a lot of well-written information on sequences and series, but the latter stages are too detailed and difficult for our course.
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