Maths Library

Number sequences and patterns: Year 11 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 11 (age 15 to 16, KS4) as a topic to introduce. 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.

  • Find the nth term of arithmetic sequences and solve problems involving specific terms.

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 11 maths

Qs
6
Marks
18
NameDateScore / 18
1.
Find the next two numbers: 15, 20, 25, 30, ,
[3]
2.
Find the next two numbers: 11, 0, −11, −22, ,
[3]
3.
Find the next two numbers: 13, 4, −5, −14, ,
[3]
4.
Find the next two numbers: 20, 11, 2, −7, ,
[3]
5.
Find the next two numbers: 1, −7, −15, −23, ,
[3]
6.
Find the next two numbers: 3, 14, 25, 36, ,
[3]

Answer key

  1. 35, 40The rule is add 5 each time; 30 then 35 then 40
  2. −33, −44The rule is subtract 11 each time; −22 then −33 then −44
  3. −23, −32The rule is subtract 9 each time; −14 then −23 then −32
  4. −16, −25The rule is subtract 9 each time; −7 then −16 then −25
  5. −31, −39The rule is subtract 8 each time; −23 then −31 then −39
  6. 47, 58The rule is add 11 each time; 36 then 47 then 58