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Recognise Other Sequences

In this worksheet, students practise recognising other types of sequences.

'Recognise Other Sequences' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Algebra

Curriculum subtopic:   Sequences

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

You have learnt now how to recognise linear sequences (such as 4, 7, 10, 13...) by the way they increase or decrease by the same amount each time.

 

If you look at the definition of a sequence though, 'a pattern of number that follows a rule', we have to look at the different types of sequence that follow different rules.

 

Fibonacci sequences: These sequences are generated by adding the previous two numbers in the sequence.

1, 1, 2, 3, 5, 8, 13, 21....

Square numbers: These are found by squaring the position of the number. So the first number is 1 x 1, the second is 2x2 etc

1, 4, 9, 16, 25, 36, 49...

Powers sequences: These are found by taking the power of a number. So the powers of 3, for example, would be 31, 32, 33, 34, 35...

3, 9, 27. 81. 243

These can be spotted quite easily as each one is a multiple of the previous one. (9 is 3 x 3, 27 is 9 x 3, 81 is 27 x 3)

Triangular Numbers. These are a bit harder to spot. Each time the difference increase by 1.

1, 3, 6, 10, 15

1 to 3 - Difference of 2

3 to 6 - Difference of 3

6 to 10 - Difference of 4

10 to 15 - Difference of 5

etc

Complete the following sentence...

Select the correct type for the sequence...

 

3, 4, 7, 11, 18...

Fibonacci

Power

Square

Triangular

Select the correct type for the sequence...

 

2, 8, 19, 32....

Fibonacci

Power

Square

Triangular

Select the correct type for the sequence...

 

2, 4, 8, 16, 32...

Fibonacci

Power

Square

Triangular

What comes next in the sequence...

 

1, 1, 2, 3, 5, 8, 13....

Fibonacci

Power

Square

Triangular

What comes next in the sequence...

 

243, 81, 27, 9....

Fibonacci

Power

Square

Triangular

Match the sequence with its type.

Match the sequence with its next number

Column A

Column B

2, 3, 5, 8, 12...
11
1, 1, 2, 3, 5, 8...
17
1, 4, 9, 16...
25

We can easily recognise a power sequence because each term is a ....

Column A

Column B

2, 3, 5, 8, 12...
11
1, 1, 2, 3, 5, 8...
17
1, 4, 9, 16...
25

The sequence 2, 3, 5, 8, 13 is called a...

Column A

Column B

2, 3, 5, 8, 12...
11
1, 1, 2, 3, 5, 8...
17
1, 4, 9, 16...
25
  • Question 1

Complete the following sentence...

CORRECT ANSWER
EDDIE SAYS
Yep, its all about adding the previous two.
  • Question 2

Select the correct type for the sequence...

 

3, 4, 7, 11, 18...

CORRECT ANSWER
Fibonacci
EDDIE SAYS
The only one this fits is fibonacci (look at a number then add the two before it)
  • Question 3

Select the correct type for the sequence...

 

2, 8, 19, 32....

CORRECT ANSWER
Power
EDDIE SAYS
This has to be a square rule. If you think about the square numbers 1, 4, 9, 16, can you see the link between this and our sequence
  • Question 4

Select the correct type for the sequence...

 

2, 4, 8, 16, 32...

CORRECT ANSWER
Power
EDDIE SAYS
Each number is double the one before, this can only be a power sequence
  • Question 5

What comes next in the sequence...

 

1, 1, 2, 3, 5, 8, 13....

CORRECT ANSWER
EDDIE SAYS
Our first step is to identify the type of sequence. This has to be a Fibonacci, so to get the next number, we add 8 and 13 and so on...
  • Question 6

What comes next in the sequence...

 

243, 81, 27, 9....

CORRECT ANSWER
EDDIE SAYS
Our first step is to identify the type of sequence. Because we are dividing by 3 each time, this has to be a powers sequence. Just keep dividing by 3 to get the next two answers.
  • Question 7

Match the sequence with its type.

CORRECT ANSWER
EDDIE SAYS
Remember to try and use a process of elimination. Powers are the easiest to see as they are just a multiplication. Suares are quite easy as they must contain square numbers (or multiples of) Fibonacci can be spotted by adding together two numbers and seeing if you get the next. Triangular will be if it doesn't fit in any of the others.
  • Question 8

Match the sequence with its next number

CORRECT ANSWER

Column A

Column B

2, 3, 5, 8, 12...
17
1, 1, 2, 3, 5, 8...
11
1, 4, 9, 16...
25
EDDIE SAYS
Remember that the first thing you need to do... 2, 3, 5, 8, 12... is a triangular sequence 1, 1, 2, 3, 5, 8... is a Fibonacci 1, 4, 9, 16... is a square sequence
  • Question 9

We can easily recognise a power sequence because each term is a ....

CORRECT ANSWER
EDDIE SAYS
Power sequences can be spotted because we multiply to get the next number. This means each term is a multiple of the previous one.
  • Question 10

The sequence 2, 3, 5, 8, 13 is called a...

CORRECT ANSWER
EDDIE SAYS
This is one of those tricky Fibonacci sequences. Remember that the way we test this is to add together two number and see if we get the next number. If we do, it\'s a Fibonacci.
---- OR ----

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