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Number sequences illustration | the nth term

Do you know how to find the rules for the n^th term?

Number Sequences 3 (Medium)

Patterns appear in nature too. This 11 Plus Maths quiz explores number sequences like the Fibonacci pattern that shapes petals, shells, and pinecones.

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Fascinating Fact:

The number of petals on many flowers follows the Fibonacci sequence, like lilies with three, buttercups with five, and daisies with thirty four.

In 11 Plus Maths, pupils learn about number sequences that build by adding or multiplying in steps. The Fibonacci sequence is a famous example found in plants, shells, and art, showing how maths connects to the natural world.

Key Terms

Fibonacci Sequence: A pattern where each number is the sum of the two before it, starting 1, 1, 2, 3, 5, 8.
Sequence: An ordered list of numbers that follow a specific rule or pattern.
Rule: The mathematical instruction used to find the next term in a sequence.

Parents can discover helpful preparation advice in our guide to 11 Plus courses and materials.

Frequently Asked Questions (Click to see answers)

What is the Fibonacci sequence in simple terms?

The Fibonacci sequence is a list of numbers where each one equals the sum of the two before it, starting 1, 1, 2, 3, 5, and so on.

Where can I see Fibonacci numbers in real life?

Fibonacci numbers appear in the spirals of pinecones, sunflower seeds, shells, and the arrangement of petals on many flowers.

Why is the Fibonacci sequence important in maths?

It shows how patterns grow naturally, helps with problem-solving, and connects maths with biology, art, and architecture.

Try These Related Quizzes

1 .

What is the rule for the n^th term in the following sequence?
7, 14, 21, 28, …

n^th term = 7n

n^th term = 6n + 1

n^th term = 8n - 1

n^th term = n⁷

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 7 = 1 x 7
n = 2, and 14 = 2 x 7
n = 3, and 21 = 3 x 7
n = 4, and 28 = 4 x 7

2 .

What is the rule for the n^th term in the following sequence?
4, 6, 8, 10, …

n^th term = 4n

n^th term = 2n + 2

n^th term = n²

n^th term = 2n - 2

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 4 = (2 x 1) + 2
n = 2, and 6 = (2 x 2) + 2
n = 3, and 8 = (2 x 3) + 2
n = 4, and 10 = (2 x 4) + 2

3 .

What is the rule for the n^th term in the following sequence?
1, 4, 9, 16, …

n^th term = n³

n^th term = 3n - 3

n^th term = n²

n^th term = 4n - 2

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 1 = 1 x 1, or 1²
n = 2, and 4 = 2 x 2, or 2²
n = 3, and 9 = 3 x 3, or 3²
n = 4, and 16 = 4 x 4, or 4²

4 .

What is the rule for the n^th term in the following sequence?
2.5, 5, 7.5, 10, …

n^th term = n + 2.5

n^th term = 2n + n

n^th term = 5n - 2

n^th term = 2.5n

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 2.5 = 1 x 2.5
n = 2, and 5 = 2 x 2.5
n = 3, and 7.5 = 3 x 2.5
n = 4, and 10 = 4 x 2.5

5 .

What is the rule for the n^th term in the following sequence?
10, 13, 16, 19, …

n^th term = 3n + 7

n^th term = n + 10

n^th term = 2n + 8

n^th term = 10n - 7

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 10 = (3 x 1) + 7
n = 2, and 13 = (3 x 2) + 7
n = 3, and 16 = (3 x 3) + 7
n = 4, and 19 = (3 x 4) + 7

6 .

What is the rule for the n^th term in the following sequence?
5, 4, 3, 2, …

n^th term = 6n - 1

n^th term = -n + 6

n^th term = 5n

n^th term = -n + 7

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 5 = -1 + 6
n = 2, and 4 = -2 + 6
n = 3, and 3 = -3 + 6
n = 4, and 2 = -4 + 6

7 .

What is the rule for the n^th term in the following sequence?
2, 6, 10, 14, …

n^th term = -n + 3n

n^th term = n + 4

n^th term = 4n - 2

n^th term = 2n

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 2 = (4 x 1) - 2
n = 2, and 6 = (4 x 2) - 2
n = 3, and 10 = (4 x 3) - 2
n = 4, and 14 = (4 x 4) - 2

8 .

What is the rule for the n^th term in the following sequence?
5, 13, 21, 29, …

n^th term = n² + 5

n^th term = 5n + 3

n^th term = 7n - 2

n^th term = 8n - 3

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 5 = (8 x 1) - 3
n = 2, and 13 = (8 x 2) - 3
n = 3, and 21 = (8 x 3) - 3
n = 4, and 29 = (8 x 4) - 3

9 .

What is the rule for the n^th term in the following sequence?
9, 15, 21, 27, …

n^th term = n + 8

n^th term = 6n + 3

n^th term = 9n

n^th term = 7n + 2

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and 9 = (6 x 1) + 3
n = 2, and 15 = (6 x 2) + 3
n = 3, and 21 = (6 x 3) + 3
n = 4, and 27 = (6 x 4) + 3

10 .

What is the rule for the n^th term in the following sequence?
-6, -7, -8, -9, …

n^th term = -n x 6

n^th term = -n - 6

n^th term = -n - 5

n^th term = n - 6

To find the rule, test each option against the numbers in the sequence. Only one will work:
n = 1, and -6 = -1 - 5
n = 2, and -7 = -2 - 5
n = 3, and -8 = -3 - 5
n = 4, and -9 = -4 - 5

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