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If a number sequence increases by one each time, the rule for the n^th term is n + 1.

Number Sequences 2 (Difficult)

Numbers, music, and nature all share patterns. This 11 Plus Maths quiz explores sequences that appear everywhere, from songs to rivers, and even in branching trees.

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Fascinating Fact:

Sequences are everywhere, from the beats in your favourite song to the way trees branch and rivers split, nature’s way of counting without a calculator.

In 11 Plus Maths, pupils study number sequences to recognise hidden patterns. Understanding how numbers build, repeat, or change helps develop logical thinking and real-world problem-solving skills.

Key Terms

Sequence: A list of numbers that follow a particular rule or pattern.
Pattern: A repeated or predictable arrangement in numbers, shapes, or sounds.
Rule: The mathematical instruction used to find the next number in a sequence.

Learn more about 11 Plus exam preparation in our guide to 11 Plus sample questions for parents.

Frequently Asked Questions (Click to see answers)

How are number sequences used in real life?

Number sequences are found in music beats, nature’s patterns, computer coding, and even in daily routines like traffic lights or timetables.

What makes a number sequence difficult?

Difficult sequences may use multiple rules, alternate between patterns, or include multiplication and division instead of simple addition or subtraction.

Why do we learn number sequences in maths?

Learning sequences strengthens logical reasoning, helps spot relationships between numbers, and prepares pupils for topics such as algebra and coding.

Try These Related Quizzes

1 .

Find the missing term.
3, 9, 15, 21, X, 33, ...

The rule for the n^th term = 6n - 3. Put in the values of 1, 2, 3, 4, ... in turn and see for yourself how the sequence is produced

2 .

Find the missing term.
32, 131, X, 329, ...

180

210

240

230

The next term is got from the previous term by adding 99, e.g. 32 + 99 = 131 and so on

3 .

Find the missing term.
-19, 4, 27, X, ...

The next term is got from the previous term by adding 23, e.g. -19 + 23 = 4 and so on

4 .

Find the missing term.
22, 8, X, -20, ...

-2

-6

The next term is got from the previous term by subtracting 14, e.g. 22 – 14 = 8 and so on

5 .

Find the missing term.
-2, 2, 6, X, ...

The rule for the n^th term = 3n + (n - 2). Put in the values of 1, 2, 3, 4, ... in turn and see for yourself how the sequence is produced

6 .

Find the missing term.
0.2, 2.4, 28.8, X, ...

57.9

123.4

288

345.6

The next term is got from the previous term by multiplying by 12, e.g. 0.2 x 12 = 2.4 and so on. You might need to use your calculator for this one!

7 .

Find the missing term.
-84, -42, -21, X, ...

-10.5

-14

-7

-8.5

The next term is got from the previous term by dividing by 2, e.g. -84 ÷ 2 = -42 and so on

8 .

Find the missing term.
1, 1.2, 1.44, X, ...

1.88

1.728

1.96

2.223

The next term is got from the previous term by multiplying by 1.2, e.g. 1.2 x 1.2 = 1.44 and so on.
Sometimes it is necessary to use your calculator!

9 .

Find the missing term.
1,000, 250, X, 15.625 ...

125

104

62.5

48.4

The next term is got from the previous term by dividing by 4, e.g. 1,000 ÷ 4 = 250 and so on

10 .

Find the missing term.
-2, 2, 6, 10, X, ...

The rule for the n^th term = 5n - (n + 2). Put in the values of 1, 2, 3, 4, ... in turn and see for yourself how the sequence is produced

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

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