### What are Number Sequences?

Number sequences are a list of numbers that are connected by a pattern.

These types of problems are fun! You need to find out what connects the numbers at each step, we call this **the rule**.

For example here is a number sequence with a missing value at the end:

A good way to work out the rule for a sequence is to **write in the gaps** between the numbers the **step** you take to get from one number to the next:

If you look at the **steps** between the numbers, we are adding 3 each time. So **the rule** is +3.

We can now work out that the missing number will be the last number in the sequence + 3:

18 + 3 = **21**

### Types of Number Sequence

Add a number

There may be the **same number** added at each step:

Or a **different number** added each time:

Subtract a number

It may be that in a sequence we **take away a number** at each step.

Or take away a **different number** at each step.

Multiply by a number

A sequence can progress by **multiplying** by a number at each step:

Divide by a number

A sequence can progress by **dividing** by a number at each step:

Fibonacci

This is a special sequence where by** the previous two numbers are added together to make the next number**:

### Picture Sequences

Sometimes number sequences are given to you as picture sequences. When this happens you simply need need to turn the pattern in to number sequences.

Example

**Question**: How many dots will there be in the next pattern in this sequence?

If we write in the number of dots in each pattern, and then work out the steps between each pattern this will help us answer the question:

Now we can see that the next pattern will have 10 + 5 = 15 dots.