Patterns and Sequences

Scheme of work: GCSE Foundation: Year 10: Term 1: Patterns and Sequences

Prerequisite Knowledge

  • use simple formulae
    • generate and describe linear number sequences
    • express missing number problems algebraically
  • Pupils need to be able to use symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:
    • missing numbers, lengths, coordinates and angles
    • formulae in mathematics and science
    • equivalent expressions (for example, a + b = b + a)
    • generalisations of number patterns

Success Criteria

  • generate terms of a sequence from either a term-to-term or a position-to-term rule
  • recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions ( r n
  • where n is an integer, and r is a rational number > 0 or a surd) and other sequences
  • deduce expressions to calculate the nth term of linear and quadratic sequences

Key Concepts

  • The nth term represents a formula to calculate any term in a sequence given its position.
  • To describe a sequence it is important to consider the differences between each term as this determines the type of pattern.
  • Quadratic sequences have a constant second difference. Linear sequences have a constant first difference.
  • Geometric sequences share common multiplying factor rather than common difference.

Common Misconceptions

  • Students often show a lack of understanding of what ‘n’ represents.
  • A sequence such as 1, 4, 7, 10 is often described as n + 3 rather than 3n – 2.
  • Quadratic sequences can involve a linear as well as a quadratic component.
  • Calculating the product of negative numbers when producing a table of results can lead to difficulty.
  • The nth term for a geometric sequence is in the form arn-1 rather than arn.

Patterns and Sequences Resources

Mr Mathematics Blog

Problem-Solving with Angles in Polygons

How to teach problem solving with angles in polygons through scaffolding.

The Sum to Infinity of Geometric Series – A-Level Maths Tutorial

Explore geometric series in our A-Level Maths tutorial. Perfect for students/teachers, with resources to download at

Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods