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Numbers sequences are just chains of numbers put together by certain rules.

Number Sequences 3 (Difficult)

Maths is hidden in flight! This 11 Plus Maths quiz explores advanced number sequences and how patterns like Fibonacci appear in nature and design.

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Fascinating Fact:

Birds flying in formation often arrange themselves in patterns based on Fibonacci angles, helping them save energy through maths.

In 11 Plus Maths, number sequences become more complex as pupils explore Fibonacci, triangular numbers, and geometric patterns. These help to strengthen reasoning and problem-solving skills by showing how patterns repeat and grow.

Key Terms

Fibonacci Sequence: A series where each number equals the sum of the two before it, starting 1, 1, 2, 3, 5, 8, and so on.
Triangular Numbers: A pattern of numbers that can form a triangle, like 1, 3, 6, 10, 15.
Geometric Sequence: A pattern where each term is multiplied by the same number to find the next.

Parents can find more guidance in our 11 Plus courses and materials guide for extra support.

Frequently Asked Questions (Click to see answers)

What is the Fibonacci sequence used for in real life?

The Fibonacci sequence appears in art, music, nature, and architecture, helping explain natural growth patterns like leaves and shells.

What is the difference between arithmetic and geometric sequences?

An arithmetic sequence adds the same amount each time, while a geometric sequence multiplies by the same number.

Why do number sequences matter in maths?

They teach pupils how to identify patterns, think logically, and prepare for more advanced topics such as algebra and coding.

Try These Related Quizzes

1 .

Which sequence can be formed from the given rule for the n^th term?
n^th term = 4n - 17

-13, -9, -5, -1, …

-21, -25, -29, -33, ...

13, 9, 5, 1, ...

21, 25, 29, 33, ...

The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = 4n - 17. As follows:
n = 1 gives (4 x 1) - 17 = -13
n = 2 gives (4 x 2) - 17 = -9
n = 3 gives (4 x 3) - 17 = -5
n = 4 gives (4 x 4) - 17 = -1

2 .

Which sequence can be formed from the given rule for the n^th term?
n^th term = -n + 20

21, 22, 23, 24, ...

19, 18, 17, 16, ...

-21, -22, -23, -24, ...

-19, -18, -17, -16, ...

the rule for the nth term = -n + 20. As follows:
n = 1 gives -1 + 20 = 19
n = 2 gives -2 + 20 = 18
n = 3 gives -3 + 20 = 17
n = 4 gives -4 + 20 = 16

3 .

Which sequence can be formed from the given rule for the n^th term?
n^th term = 2.5n + 22

19.5, 22, 24.5, 27, ...

22.5, 25, 27.5, 30, ...

24.5, 27, 29.5, 32, …

25, 27.5, 30, 32.5, ...

The terms of the sequence are found by first putting n = 1, then n = 2, then n = 3 and finally n = 4 in the rule for the nth term = 2.5n + 22. As follows:
n = 1 gives (2.5 x 1) + 22 = 24.5
n = 2 gives (2.5 x 2) + 22 = 27
n = 3 gives (2.5 x 3) + 22 = 29.5
n = 4 gives (2.5 x 4) + 22 = 32

4 .

What is the rule for the n^th term in the following sequence?
8, 12, 16, 20, …

n^th term = 5n + 2

n^th term = 8n

n^th term = 5n - 2

n^th term = 4n + 4

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 8 = (4 x 1) + 4
n = 2, and 12 = (4 x 2) + 4
n = 3, and 16 = (4 x 3) + 4
n = 4, and 20 = (4 x 4) + 4

5 .

What is the rule for the n^th term in the following sequence?
27, 26, 25, 24, …

n^th term = -n + 28

n^th term = 9n

n^th term = -n + 30

n^th term = 7n + 20

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 27 = -1 + 28
n = 2, and 26 = -2 + 28
n = 3, and 25 = -3 + 28
n = 4, and 24 = -4 + 28

6 .

What is the rule for the n^th term in the following sequence?
-1, -2, -3, -4, …

n^th term = n - n

n^th term = n - 2n

n^th term = -n²

n^th term = -n - n

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and -1 = 1 - (2 x 1)
n = 2, and -2 = 2 - (2 x 2)
n = 3, and -3 = 3 - (2 x 3)
n = 4, and -4 = 4 - (2 x 4)
Of course, -n would work too, but that wasn’t one of the options!

7 .

Find the missing term.
88, X , 122, 139, …

110

108

105

100

The values are increasing by 17 as the sequence continues:
88 + 17 = 105
105 + 17 = 122
122 = 17 = 139, etc…

8 .

Find the missing term.
-22, -26.5, X, -35.5, …

-29.5

-30

-30.5

-31

The values are decreasing by 4.5 as the sequence continues:
-22 - 4.5 = -26.5
-26.5 - 4.5 = -31
-31 - 4.5 = -35.5, etc…

9 .

Find the missing term.
0.5, 2, 4.5, X, 12.5, 18, …

6.5

7.5

This one was very tricky, so well done if you got it right.
The rule for this sequence is the n^th term = n² ÷ 2:
1² ÷ 2 = 0.5
2² ÷ 2 = 2
3² ÷ 2 = 4.5
4² ÷ 2 = 8
5² ÷ 2 = 12.5
6² ÷ 2 = 18, etc…

10 .

Find the missing term.
5.5, 6, X, 7, …

6.25

6.5

6.75

6.9

The sequence is increasing by 0.5 as it progresses:
5.5 = 0.5 = 6
6 + 0.5 = 6.5
6.5 + 0.5 = 7, etc…

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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