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If the n^th term = 5n, simply multiply n by 5.

Number Sequences 2 (Medium)

Maths and sport both follow patterns. This 11 Plus Maths quiz helps you explore how tournaments, rounds, and scores can all form number sequences.

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Fascinating Fact:

In sports tournaments, the number of matches forms a pattern, doubling each round until only one winner is left.

In 11 Plus Maths, pupils learn to recognise sequences that increase or decrease by a fixed rule. Understanding these patterns builds logic and supports problem-solving across many subjects, including sports and science.

Key Terms

Geometric Sequence: A pattern where each term is multiplied by the same number, such as 2, 4, 8, 16.
Term: Each individual number in a sequence that follows a specific rule.
Progression: A sequence that develops steadily by adding, subtracting, or multiplying by a fixed value.

Find more 11 Plus preparation materials in our guide to 11 Plus sample questions for parents.

Frequently Asked Questions (Click to see answers)

How are number sequences used in tournaments?

In knockout tournaments, each round halves the number of players, creating a pattern that continues until one winner remains.

What is the difference between arithmetic and geometric sequences?

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

Why are sequences important in problem-solving?

Recognising patterns helps pupils predict outcomes, plan strategies, and apply logical thinking to mathematical and real-life situations.

Try These Related Quizzes

1 .

Which sequence can be formed from the given rule for the n^th term?.
n^th term = 3n + 2

5, 8, 11, 14 ...

7, 9, 11, 14 ...

5, 9, 11, 14

5, 8, 11, 15

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 n^th term = 3n + 2. As follows (do the multiplication first THEN the addition):
n = 1 gives 3 × 1 + 2 = 5
n = 2 gives 3 × 2 + 2 = 8
n = 3 gives 3 × 3 + 2 = 11
n = 4 gives 3 × 4 + 2 = 14

2 .

Which sequence can be formed from the given rule for the n^th term?.
n^th term = n³

1, 4, 9, 12 ...

1, 8, 27, 64 ...

3, 6, 9, 12 ...

3, 9, 16, 25 ...

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 n^th term = n³. As follows:
n = 1 gives 1³ = 1
n = 2 gives 2³ = 8
n = 3 gives 3³ = 27
n = 4 gives 4³ = 64

3 .

Which sequence can be formed from the given rule for the n^th term?.
n^th term = 2n - n

0, 1, 2, 3 ...

1, 3, 5, 7 ...

1, 2, 3, 4 ...

0, 2, 4, 6 ...

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 n^th term = 2n - n. As follows (do the multiplication first THEN the subtraction):
n = 1 gives 2 x 1 - 1 = 1
n = 2 gives 2 x 2 - 2 = 2
n = 3 gives 3 x 2 - 3 = 3
n = 4 gives 4 x 2 - 4 = 4

4 .

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

0, 4, 8, 12 ...

0, -4, -8, -12 ...

-4, -6, -8, -10

-4, -8, -12, -16 ...

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 n^th term = -4n. As follows:
n = 1 gives -4 × 1 = -4
n = 2 gives -4 × 2 = -8
n = 3 gives -4 × 3 = -12
n = 4 gives -4 × 4 = -16

5 .

Which sequence can be formed from the given rule for the n^th term?.
n^th term = 3n + 10

13, 16, 19, 22 ...

3, 6, 9, 12 ...

13, 15, 18, 21 ...

13, 16, 18, 22 ...

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 n^th term = 3n + 10. As follows (do the multiplication first THEN the addition):
n = 1 gives 3 × 1 + 10 = 13
n = 2 gives 3 × 2 + 10 = 16
n = 3 gives 3 × 3 + 10 = 19
n = 4 gives 3 × 4 + 10 = 22

6 .

Which sequence can be formed from the given rule for the n^th term?.
n^th term = 12n

1, 12, 24, 36 ...

12, 24, 36, 48 ...

12, 24, 38, 48 ...

12, 24, 36, 49 ...

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 n^th term = 12n. As follows:
n = 1 gives 12 × 1 = 12
n = 2 gives 12 × 2 = 24
n = 3 gives 12 × 3 = 36
n = 4 gives 12 × 4 = 48

7 .

Which sequence can be formed from the given rule for the n^th term?.
n^th term = -n + 3

4, 5, 6, 7 ...

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

2, 1, 0, -1 ...

1, 0, -1, -2 ...

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 n^th term = -n + 3. As follows:
n = 1 gives -1 + 3 = 2
n = 2 gives -2 + 3 = 1
n = 3 gives -3 + 3 = 0
n = 4 gives -4 + 3 = -1

8 .

Which sequence can be formed from the given rule for the n^th term?.
n^th term = 3n + 7

7, 10, 13, 16 ...

10, 15, 20, 25 ...

7, 14, 21, 28 ...

10, 13, 16, 19 ...

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 n^th term = 3n + 7. As follows (do the multiplication first THEN the addition):
n = 1 gives 3 × 1 + 7 = 10
n = 2 gives 3 × 2 + 7 = 13
n = 3 gives 3 × 3 + 7 = 16
n = 4 gives 3 × 4 + 7 = 19

9 .

Which sequence can be formed from the given rule for the n^th term?.
n^th term = 9n – 5

4, 13, 22, 31 ...

5, 14, 23, 32 ...

3, 12, 21, 30 ...

6, 15, 24, 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 n^th term = 9n -5. As follows (do the multiplication first THEN the subtraction):
n = 1 gives 9 × 1 - 5 = 4
n = 2 gives 9 × 2 - 5 = 13
n = 3 gives 9 × 3 - 5 = 22
n = 4 gives 9 × 4 - 5 = 31

10 .

Which sequence can be formed from the given rule for the n^th term?.
n^th term = 1.5n

0.5, 2, 3.5, 5 ...

1.5, 3, 4.5, 6 ...

3, 6, 9, 12 ...

15, 30, 45, 60 ...

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 n^th term = 1.5n. As follows:
n = 1 gives 1.5 × 1 = 1.5
n = 2 gives 1.5 x 2 = 3
n = 3 gives 1.5 × 3 = 4.5
n = 4 gives 1.5 × 4 = 6

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