Maths Library

Number sequences and patterns: Year 8 maths

This topic covers identifying pattern rules, continuing numerical sequences, and finding missing terms. The worksheet reinforces recognition of arithmetic, geometric, and special sequences like square numbers.

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What this covers

Number sequences and patterns is taught in Year 8 (age 12 to 13, KS3) as a main teaching focus. It sits in the Algebra strand.

Worked example

Find the next two terms in the sequence: 4, 9, 14, 19, ...

  1. Find the difference between consecutive terms: 9 - 4 = 5, 14 - 9 = 5
  2. Add 5 to the fourth term: 19 + 5 = 24
  3. Add 5 to the fifth term: 24 + 5 = 29

Answer: 24, 29

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Simple ascending linear sequences with step sizes of 2, 5, or 10
  2. Linear sequences with arbitrary integer additions or subtractions
  3. Sequences involving negative numbers or descending patterns
  4. Simple geometric sequences involving doubling, tripling, or halving
  5. Non-linear sequences including square numbers, triangular numbers, or Fibonacci-type patterns

Common mistakes

  • Assuming all sequences are arithmetic and searching only for a constant difference
  • Subtracting the wrong way around when determining the common difference in descending sequences

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Generate terms of a sequence and find the nth term of a linear sequence.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Number sequences and patterns

Year 8 maths

Qs
6
Marks
12
NameDateScore / 12
1.
Find the next two numbers: 15, 19, 23, 27, ,
[2]
2.
Find the next two numbers: 11, 1, −9, −19, ,
[2]
3.
Find the next two numbers: 13, 5, −3, −11, ,
[2]
4.
Find the next two numbers: 20, 12, 4, −4, ,
[2]
5.
Find the next two numbers: 1, −7, −15, −23, ,
[2]
6.
Find the next two numbers: 3, 13, 23, 33, ,
[2]

Answer key

  1. 31, 35The rule is add 4 each time; 27 then 31 then 35
  2. −29, −39The rule is subtract 10 each time; −19 then −29 then −39
  3. −19, −27The rule is subtract 8 each time; −11 then −19 then −27
  4. −12, −20The rule is subtract 8 each time; −4 then −12 then −20
  5. −31, −39The rule is subtract 8 each time; −23 then −31 then −39
  6. 43, 53The rule is add 10 each time; 33 then 43 then 53