Numbers written in a specific order can form a sequence. Terms in a sequence can be related by patterns such as a common difference. Sequences where terms have a common difference are called 'arithmetic sequences.'

A **sequence** is a **set of numbers** arranged in a specific order.

A sequence has some key features:

- Each
**number**in a sequence is called a**term**of the sequence - Each
**term**has a**position**, eg 1st, 2nd, 3rd etc - The
**terms**are linked by a**pattern**or**rule** - The three dots at the end,
**...**, show that the sequence can keep going and more terms worked out

Here are some well-known number sequences that you should learn to recognise:

The **terms** are **2, 4, 6, 8...**

Their **positions** are **1st, 2nd, 3rd, 4th...**

To find the next term the **rule** is **+2**

- Question
What are the

**5th**and**6th**terms?**5th term = 4th term + 2****= 8 + 2****= 10****6th term = 5th term + 2****= 10 + 2****= 12**

The **terms** are **1, 3, 5, 7...**

The **positions** are **1st, 2nd, 3rd, 4th...**

To find the next term the **rule** is **+2**

- Question
What are the

**5th**and**6th**terms?**5th term = 4th term + 2****= 7 + 2****= 9****6th term = 5th term + 2****= 9 + 2****= 11**

The **terms** are **1, 4, 9, 16...**

The **positions** are **1st, 2nd, 3rd, 4th...**

The rule is each **term** is formed by multiplying the **position** by itself:

- Question
What are the

**5th**and**6th**terms?**5th term = 5 x 5****= 25****6th term = 6 x 6****= 36**

The **terms** are **1, 8, 27, 64...**

The **positions** are **1st, 2nd, 3rd, 4th...**

The rule is each **term** is formed by multiplying the **position** by itself three times:

- Question
What are the

**5th**and**6th**terms?**5th term = 5 x 5 x 5****= 125****6th term = 6 x 6 x 6****= 216**

The **terms** are **1, 3, 6, 10...**

The **positions** are **1st, 2nd, 3rd, 4th...**

The **rule** is that each term is **previous term + position**, eg:

**4th term = 3rd term + 4**

- Question
What are the

**5th**and**6th**terms?**5th term = 4th term + 5****= 10 + 5****= 15****6th term = 5th term + 6****= 15 + 6****= 21**

The **terms** are **2, 4, 8, 16...**

(2, 2 x 2, 2 x 2 x 2, 2 x 2 x 2 x 2...)

The **positions** are **1st, 2nd, 3rd, 4th...**

To find the next term, the **rule** is **x 2**

- Question
What are the

**5th**and**6th**terms?**5th term = 4th term x 2****= 16 x 2****= 32****6th term = 5th term x 2****= 32 x 2****= 64**

The **terms** are **10, 100, 1000, 10000...**

(10, 10 x 10, 10 x 10 x 10, 10 x 10 x 10 x 10...)

The **positions** are **1st, 2nd, 3rd, 4th...**

To find the next term, the **rule** is **x 10**

- Question
What are the

**5th**and**6th**terms?**5th term = 4th term x 10****= 10,000 x 10****= 100,000****6th term = 5th term x 10****= 100,000 x 10****= 1,000,000**