Sequences and Patterns

Spotting the pattern is a core maths skill - from the way a savings club's contributions grow to the number of desks needed as a classroom adds more rows. This topic covers number sequences and their rules.

  • Term-to-term and position-to-term rules
  • Arithmetic sequences
  • Simple quadratic sequences

Lessons for Sequences and Patterns

Term-to-Term and Position-to-Term Rules

Two ways to describe a patternTerm-to-term: how to get the next term from the one before - like each round …

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Arithmetic Sequences

Constant differenceAn arithmetic sequence adds (or subtracts) the same amount every time - the "common difference", like a fixed weekly …

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Simple Quadratic Sequences

When the difference itself changes steadilyIf the differences between terms aren't constant, but the differences of the differences are, the …

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Exercises for Sequences and Patterns

Find the rules

Write the term-to-term rule for 2, 5, 8, 11,...Find the next two terms of 100, 90, 80, 70,...Find the nth …

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Arithmetic sequence problems

Find the 15th term of the sequence with a = 4, d = 3.Find the nth term of 8, 13, …

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Quadratic sequence problems

Find the next two terms of 2, 5, 10, 17, 26,...Show that the sequence 1, 4, 9, 16,... has a …

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