Patterns and Sequences

Students learn how to generate and describe sequences on a term-to-term and position-to-term basis.Ā  Learning progresses from plotting and reading coordinates in the first quadrant to describing geometric sequences using the nth term.

This unit takes place in Term 1 of Year 10 and is followed by the properties of straight line graphs.


Patterns and Sequences Lessons


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 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 for what ā€˜nā€™ represents.
  • A sequence such as 1, 4, 7, 10 is often described as n + 3 rather than 3n ā€“ 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.

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