# Linear sequences

**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 ***n*th term of a linear sequence

*n*th term of a linear sequence

To find the *n*th 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:

= 3*n +* 1

**Plotting terms**

The *n*th 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 = 2*n* + 1