# Mixed Sequences

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

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Generate Terms of a Sequence

Difficulty level:

### 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 ...

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...

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 ...

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 ...

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 ...

-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 ...

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 ...

-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 ...

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 ...

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 ...

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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