A sequence is a set of numbers arranged in a particular order.
Sequences can be:
finite, a fixed number of terms e.g 3, 4
infinite, going on forever e.g. 3, 4, 5, 6,...
This course studies infinite sequences.
Many sequences have a mathematical pattern.
Arithmetic and Geometric sequences are examples of sequences with a patterns and are studied in the next two topics. Sequences can be enclosed in triangular brackets. <3, 4, 5...>
Each number in a sequence is called a term. There are various ways of describing terms.
The first term of a sequence can be given by t1, t(1), T(1) or T1. We will use t1.
The general term or n th term is written as t n.
There are four ways to express a sequence.
|By listing||List the first four or five terms in order.||2, 8, 23, 68...|
|By formula for the nth term||
A formula is provided to work out any term of the sequence.
This activity will help you to work out the formula for sequences.
<3n + 2> or tn = 3n + 2First term, t1 = 3 x 1 + 2 = 5
Second term, t2 = 3 x 2 + 2 = 8
Third term t3 = 3 x 3 + 2 = 11 etc.
The sequence is 5, 8, 11...
|By a recursive function||
One term is provided and a formula is given to work out the following term.
t 1 = 3 ,t n + 1 = 2 t n + 1
First term is 3
The sequence is 3, 7, 15...
The sequence is illustrated on a graph.
The horizontal axis is the number of the term.
The vertical axis is the term itself.
Graph < 1, 3, 5, 7... >