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Recognise and Continue Linear Sequences

In this worksheet, students will recognise and continue simple linear sequences.

'Recognise and Continue Linear Sequences' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, OCR, Pearson Edexcel

Curriculum topic:   Algebra

Curriculum subtopic:   Sequences

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

When we are dealing with sequences, it helps to understand what a sequence is.

It is just a set of numbers that follow a rule.

 

In this activity, we are going to look at linear sequences. These are sequences that are increasing or decreasing by the same amount each time

 

Example 1: For the sequence 7, 9, 11, 13. Give the next two terms and the rule.

We need to look at the difference for this, the difference is always 2 between the terms and it is going up, so the rule is +2

To get the next two terms, we just apply the rule twice, this will give 15 and 17

 

Example 2: How many lines will be in the next diagram?

Whenever we have a question like this, where a sequence is drawn instead of given as numbers, our first step is to always turn it into a sequence that contains numbers.

If we just count the lines in each diagram, we get the following sequence...

4, 7, 10, 13

So the rule is +3 and the next diagram will have 16 lines. You might also be asked to draw it (but im sure you can do that!)

 

What are the next two terms in the sequence...

1,3,5,7....

Match the sequence with its rule

Column A

Column B

1, 4, 7, 10
-3
2, 4, 6, 8
+ 3
10, 7, 4, 1
+ 0
1, 1, 1, 1
+ 2

Which of the following rules could describe the sequence...

 

3, 7, 11, 15...

x 2

+ 4

- - 4

+ 5

Which of the following patterns could be correct for the sequence...

10, 8, 6, 4...

+ 2

- 2

- - 2

- + 2

How many lines will be in the next diagram for the sequence...

How many lines will be in the 6th diagram for the sequence...

For each sequence, click the box that describes if the rule is correct or incorrect.

True or False?

 

A sequence can only be increased or decreased by the same amount each time.

True

False

What are the next three terms in this sequence?

25, 22, 19, __, __, __

True

False

Complete the following sentence...

True

False

  • Question 1

What are the next two terms in the sequence...

1,3,5,7....

CORRECT ANSWER
EDDIE SAYS
Did you look at the difference between the terms to find the rule? We have to add 2 each time.
  • Question 2

Match the sequence with its rule

CORRECT ANSWER

Column A

Column B

1, 4, 7, 10
+ 3
2, 4, 6, 8
+ 2
10, 7, 4, 1
-3
1, 1, 1, 1
+ 0
EDDIE SAYS
Just remember you have to look at the differences between the numbers. If it's going up it's a plus and if it's going down, it's a minus.
  • Question 3

Which of the following rules could describe the sequence...

 

3, 7, 11, 15...

CORRECT ANSWER
+ 4
- - 4
EDDIE SAYS
I sure you spotted one of the rules quite easily, did you notice the other? Remember that - and - is the same as +
  • Question 4

Which of the following patterns could be correct for the sequence...

10, 8, 6, 4...

CORRECT ANSWER
- 2
- + 2
EDDIE SAYS
Did you get it this time? We are going down by 2 so our rule must work out as - 2
  • Question 5

How many lines will be in the next diagram for the sequence...

CORRECT ANSWER
9
EDDIE SAYS
If we start by turning this into a number sequence, I get... 3, 5, 7... The next one will follow this rule of increasing by 2 each time.
  • Question 6

How many lines will be in the 6th diagram for the sequence...

CORRECT ANSWER
19
EDDIE SAYS
The common mistake here is to count the number of lines in the 3rd diagram and double it to find the 6th. Unfortunately, it's not quite that simple, we have to make a sequence before we can do this. We have... 4, 7, 10 We just need to keep this going until we find the 6th number
  • Question 7

For each sequence, click the box that describes if the rule is correct or incorrect.

CORRECT ANSWER
EDDIE SAYS
It's really easy to make a mistake if you're rushing. Remember that if it's going down, it will be negative
  • Question 8

True or False?

 

A sequence can only be increased or decreased by the same amount each time.

CORRECT ANSWER
False
EDDIE SAYS
We have only dealt with ones that increase or decrease by the same. This doesn't mean nothing else could happen. Think about the sequence 2, 4, 8, 16. Does this have a rule?
  • Question 9

What are the next three terms in this sequence?

25, 22, 19, __, __, __

CORRECT ANSWER
EDDIE SAYS
Did you spot the rule? Each term is going down by 3.
  • Question 10

Complete the following sentence...

CORRECT ANSWER
EDDIE SAYS
We need to make sure we use the correct vocab when dealing with these. The correct way to say \'look at how much it goes up each time\' is \'find the difference\'
---- OR ----

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