This KS3 Maths quiz looks at lists of numbers which follow a clear pattern or sequence. For example: 1, 3, 5 and 7 are the first four odd numbers or 15, 20, 25 and 30 are all going up in 5s. But the questions below are not quite as easy as that! Well, you wouldn't want them to be, would you?

Finding out the rule in a number sequence takes a bit of detective work. First, work out the difference between each consecutive number. Are they increasing or decreasing? If the difference is always the same, then you've found the rule. If the numbers go up or down by a different amount each time then things are a little trickier. Make a note of each number change and then compare them. Are they doubling, trebling or something else?

It will help you in algebra if you to practise finding numbers in patterns. The better you get at spotting how the patterns are formed, then the better you will be at maths. Take your time and make sure you understand each question before you submit your answers. Good luck!

1.

An ordered set of numbers that follow a pattern is called what?

A Secret

A Sequel

A Sequence

A Sequin

A sequence is a particular order in which related things follow each other

2.

When numbers are put together in such a way that they follow a pattern, they are said to follow a what?

Riley

Roller

Rule

Ruler

The rule might be 'add four' or 'double the last number' for example

3.

Each number in a sequence is called a(n) …….

Unit

Term

Item

Position

Terms in a sequence are often labelled Tn where n indicates the position of the term in the sequence: for the 1st term, n = 1, for the 2nd n = 2 etc

4.

What are the next three numbers in this sequence: 28, 24, 20, 16?

14, 12, 10

15, 14, 13

20, 24, 28

12, 8, 4

Each number is 4 less than the previous number. If asked to give the rule we might say 'Take 4 from the previous number'

5.

What are the 3 missing numbers in the following sequence 3, 6, ....... , ....... , ....... , 18, 21, 24?

7, 8, 9

8, 10, 14

9, 12, 15

3, 6, 12,

The rule is that we add 3 to the previous number

6.

What is the rule in the following sequence 2, 4, 8, 16, 32, 64, 128?

Add 8 to the previous number

Add together the two previous numbers

Double the previous number

Halve the previous number

If you carried this sequence on the numbers would soon become astronomical!

7.

Which numbers come next in the following sequence: 1, 1, 2, 3, 5, 8?

13, 21, 34

11, 14, 17

5, 3, 2

12, 20, 30

This sequence is called the Fibonacci sequence. The rule is that we add together the two previous numbers. Sometimes sequences are easy to spot and at other times they take a lot of thinking about!

8.

What is the nth term (Tn) in the sequence 1, 2, 3, 4, 5, …….?

9

n

n + 1

n - 1

These are simply the counting numbers. The first term is 1; the second term is 2; the third term is 3 etc., so the nth term, Tn, is just n

9.

What is the nth term in this sequence: 4, 7, 10, 13, …….?

n + 4

3n + 1

2n + 2

5n - 1

Try out each rule to find which fits. If Tn = 3n + 1, when n = 1 the 1st term is 3 x 1 + 1 = 4 but if Tn = n + 4, the 1st term is 1 + 4 = 5

10.

What is the sixth term in the sequence with Tn = 2n - 5?

7

10

17

27

Use n = 6 to find the value of Tn

The next step is:

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