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Mixed Sequences

In this worksheet, students find the given term in sequences.

'Mixed Sequences' worksheet

Key stage:  KS 2

Curriculum topic:  Maths and Numerical Reasoning

Curriculum subtopic:  Sequences

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

You should already know about the Fibonacci sequence, which goes like this:

 

1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ...

 

And Arithmetic sequences like this:

 

4, 10, 16, 22, 28, 34 ...

 

And Geometric sequences like this:

 

4, 20, 100, 500, 2500 ...

 

 

And the Square Number sequence like this:

 

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

 

 

In this worksheet, you must count on and state the given term.

Work out the 7th term in this Fibonacci sequence:

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

Work out the 7th term in this arithmetic sequence:

 5, 8, 11, 14, 17...

Work out the 7th term in this arithmetic sequence:

 1, 2, 4, 8, 16 ...

Work out the 7th term in this sequence:

 5, 8, 13, 21, 34 ...

Work out the 7th term in this sequence:

 5, 2, -1, -4, -7 ...

Work out the 7th term in this sequence:

 1920, 960, 480, 240, 120 ...

Work out the 7th term in this sequence:

 5, -5, 0, -5, -5 ...

Work out the 10th term in this sequence:

 1, 4, 7, 10, 13 ...

Work out the 10th term in this sequence:

3, 6, 12, 24, 48 ...

Work out the 10th term in this sequence:

 1, 4, 9, 16, 25 ... 

  • Question 1

Work out the 7th term in this Fibonacci sequence:

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

CORRECT ANSWER
21
EDDIE SAYS
The fibonacci sequence is generated by adding the previous two terms together. We have 6 terms in this sequence so we are just looking for the next term which will be given by 8 + 13 = 21
  • Question 2

Work out the 7th term in this arithmetic sequence:

 5, 8, 11, 14, 17...

CORRECT ANSWER
23
EDDIE SAYS
The pattern here is to add three each time. We have five terms and we are looking for the 7th term so we need to add on 2 terms. 17 + 3 = 20 20 + 3 = 23
  • Question 3

Work out the 7th term in this arithmetic sequence:

 1, 2, 4, 8, 16 ...

CORRECT ANSWER
64
EDDIE SAYS
The pattern here is to double the number each time We have five terms and we are looking for the seventh so we need to double twice. 16 x 2 = 32 32 x 2 = 64
  • Question 4

Work out the 7th term in this sequence:

 5, 8, 13, 21, 34 ...

CORRECT ANSWER
89
EDDIE SAYS
If you look at the differences between the numbers here you will notice there isn\'t a set pattern (+3, + 5 + 8 + 13) so we need to look and see if this is a fibonacci sequence (Yes, it is) We add the previous two numbers together to find the next number. 21 + 34 = 55 34 + 55 = 89
  • Question 5

Work out the 7th term in this sequence:

 5, 2, -1, -4, -7 ...

CORRECT ANSWER
-13
EDDIE SAYS
The pattern here is subtract 3. -7 - 3 = -10 -10 - 3 = -13
  • Question 6

Work out the 7th term in this sequence:

 1920, 960, 480, 240, 120 ...

CORRECT ANSWER
30
EDDIE SAYS
The pattern here is that we are dividing by two each time. 120 ÷ 2 = 60 60 ÷ 2 = 30
  • Question 7

Work out the 7th term in this sequence:

 5, -5, 0, -5, -5 ...

CORRECT ANSWER
-15
EDDIE SAYS
Once again this is a fibonnaci sequence. -5 + -5 = -10 -5 + -10 = -15
  • Question 8

Work out the 10th term in this sequence:

 1, 4, 7, 10, 13 ...

CORRECT ANSWER
28
EDDIE SAYS
The pattern here is add 3. Be careful here that the question is now asking for the 10th term so we need to add 5 more terms. 13 + 3 = 16 16 + 3 = 19 19 + 3 = 22 22 + 3 = 25 25 + 3 = 28
  • Question 9

Work out the 10th term in this sequence:

3, 6, 12, 24, 48 ...

CORRECT ANSWER
1536
EDDIE SAYS
The pattern here is multiply by 2. Once again we are looking for the 10th term so we need to find the next 5 numbers 48 x 2 = 96 96 x 2 = 192 192 x 2 = 384 384 x 2 = 768 768 x 2 = 1536
  • Question 10

Work out the 10th term in this sequence:

 1, 4, 9, 16, 25 ... 

CORRECT ANSWER
100
EDDIE SAYS
This one can be a tricky one of you don\'t know it. These numbers are the square numbers. We are looking for the 10th square number 6 x 6 = 36 7 x 7 = 49 8 x 8 = 64 9 x 9 = 81 10 x 10 = 100
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