 # Fibonacci Sequences

In this worksheet, students find the missing term in Fibonacci sequences. Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Generate Terms of a Sequence

Difficulty level:   ### QUESTION 1 of 10

Fibonacci was an Italian mathematician from Pisa, who invented the following sequence in the year 1202:

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

After the first two terms, each term is formed by adding the two previous terms.

So here,

2 = 1 + 1

3 = 2 + 1

5 = 3 + 2

8 = 5 + 3

13 = 8 + 5 etc...

Fibonacci used 1 and 1 as his starting numbers, but any two numbers can be used.

Example

Work out the missing term in this Fibonacci sequence:

2, 2, 4, ?, 10, 16 ...

Look at the first two terms, which add to give 4, the third term.

The missing term is therefore 2 + 4 = 6

Check that the next terms works too

4 + 6 = 10

6 + 10 = 16

Work out the missing term in this Fibonacci sequence:

1, 2, 3, ?, 8, 13 ...

Work out the missing term in this Fibonacci sequence:

-2, 2, 0, ?, 2, 4 ...

Work out the missing term in this Fibonacci sequence:

5, 2, 7, ?, 16, 25 ...

Work out the missing term in this Fibonacci sequence:

3, 9, 12, ?, 33, 54...

Work out the missing term in this Fibonacci sequence:

1, 6, 7, ?, 20, 33 ...

Work out the missing term in this Fibonacci sequence:

3, ?, 8, 13, 21, 34 ...

Work out the missing term in this Fibonacci sequence:

7, ?, 19, 31, 50, 81...

Work out the missing term in this Fibonacci sequence:

-3, ?, 2, 7, 9, 16 ...

Work out the missing term in this Fibonacci sequence:

0, -15, -15, ?, -45, -75 ...

Work out the missing term in this Fibonacci sequence:

5, -7, ?, -9, -11...

• Question 1

Work out the missing term in this Fibonacci sequence:

1, 2, 3, ?, 8, 13 ...

5
• Question 2

Work out the missing term in this Fibonacci sequence:

-2, 2, 0, ?, 2, 4 ...

2
• Question 3

Work out the missing term in this Fibonacci sequence:

5, 2, 7, ?, 16, 25 ...

9
• Question 4

Work out the missing term in this Fibonacci sequence:

3, 9, 12, ?, 33, 54...

21
• Question 5

Work out the missing term in this Fibonacci sequence:

1, 6, 7, ?, 20, 33 ...

13
• Question 6

Work out the missing term in this Fibonacci sequence:

3, ?, 8, 13, 21, 34 ...

5
• Question 7

Work out the missing term in this Fibonacci sequence:

7, ?, 19, 31, 50, 81...

12
• Question 8

Work out the missing term in this Fibonacci sequence:

-3, ?, 2, 7, 9, 16 ...

5
• Question 9

Work out the missing term in this Fibonacci sequence:

0, -15, -15, ?, -45, -75 ...

-30
• Question 10

Work out the missing term in this Fibonacci sequence:

5, -7, ?, -9, -11...

-2
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