GCSE Maths (AQA)

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nth Term of a Quadratic Sequence

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Algebra Sequences

nth Term of a Quadratic Sequence

7:12 Arithmetic & Quadratic Sequences
Spec A25
Previous Quadratic Sequences Next Introduction to Ratios
  • Differences between successive terms in a quadratic sequence will all be different
  • The differences between these differences will all be the same
  • The coefficient of the n squared term in the expression for the sequence's nth term will be half of the second difference
  • Subtracting the n squared term from each term in the sequence will create a new arithmetic sequence
  • The formula to produce an arithmetic sequence is b n plus c
  • The coefficient of n squared in the nth term expression can be found by halving the second difference
  • Subtract the n squared part of the nth term expression from each term to find a new arithmetic sequence
  • Find the common difference between the terms of the arithmetic sequence
  • The coefficient of n in the nth term expression is the common difference of the arithmetic sequence
  • Equate the incomplete nth term expression to a term in the sequence to find the value of C
  • Write out the full expression for the nth term: 3n squared plus 5n plus 1

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