# Generating sequences from rules

**Sequences**

**Sequences** is a list of numbers which follow a certain rule set. In sequences, each number is called a **term **and terms next to each other are called **consecutive terms**. When solving sequences, it is also important to know the position of the terms to help with the definition of the sequence.

For example:

2, 5, 8, 11, 14, 17, 20……..

2 – is the first term

17 – is the sixth term

** Sequences from term-to-term rules**

To define a **term-to term** sequence, the first term is needed to know what is done to give the next term.

For example:

-7, -4, -1, 2, 5

The first term is **-7** and the term-to-term rule is “plus 3.”

**Sequences from position-to-term rules**

To define a **position-to-term rule **a formula is used to determine the *n*th term of the sequence.

In this scenario, it is suggested that the terms are inserted into a table.

In this example the *n*th term of the sequence is *n²*

**Writing sequences from position-to-term rules**

The *n*th term is also called the **general term** which is also represented as . Therefore the following is true:

1st term is called U1, 2nd term is called U2 etc.

For example:

If the *n*th term of a sequence is 5*n* – 6 then the rule is written as:

= 5*n* – 6