Generating linear sequences
When the difference between each term is a sequence is always the same, this is called a linear or an arithmetic sequence.
In linear sequences, the constant difference between the consecutive terms is called the common difference, d.
The first term in a linear sequence is called a.
When the values of a and d are provided, they can be used to generate a sequence.
For example, if a = 5 and d = –3, we have the sequence:
5, 2, -1, -4, -7, -10,
The nth term of a linear sequence
To find the nth term, , of the following sequence is deduced using the following method:
4, 7, 10, 13, 16…
In this example, the common difference d is 3 (this is the multiple of 3)
Therefore this is written as:
= 3n + 1
The nth term of a linear sequence can also be plotted on a graph. These are plotted on a straight line and the equation can be written in the y = mx + c form.
The sequence 3,5,7,9,11 can be shown graphically as follows:
Here the graph represents = 2n + 1