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Sequences

infoWhy this? Fractional and non-linear sequences broaden our understanding of how patterns can be represented and tested algebraically. Using nth-term rules to generate terms or determine membership develops generalisation, substitution, and proof-like reasoning.

scheduleWhy now? Earlier sequence units secured arithmetic patterns, decreasing sequences, and introductory non-linear rules. Year 9 extends these methods to fractional expressions and more varied functions before deeper work with quadratic sequences and graphs.

neurologyYou need to know

  • A sequence is an ordered list of numbers in which each term is defined by its position, `n`, in the sequence.
  • The nth term of a sequence is a formula that allows any term in the sequence to be calculated from its position, `n`.
  • A fractional sequence is a sequence in which the terms are fractions, and its nth term may be expressed as a fractional algebraic expression.
  • Non-linear sequences are sequences in which the nth term is not a linear function of `n`, such as quadratic, cubic, or other non-linear forms.
  • A number is a term in a sequence if solving the nth term formula for `n` gives a positive integer.
  • The first five terms of a sequence correspond to `n = 1, 2, 3, 4, 5` in the nth term formula.
  • The nth term formula for a non-linear sequence may involve powers or other non-linear operations on `n`.
  • Any term in a sequence can be found by substituting its position, `n`, into the nth term formula.

rocket_launchYou must be able to

  • Substitute a given value into the nth term formula, including fractional and non-linear forms, to calculate a specific term in the sequence.
  • Solve equations involving the nth term formula to determine whether a given number is a term in the sequence by solving for `n` and checking whether it is a positive integer.
  • Derive the nth term of a fractional sequence from a given pattern or list of terms.
  • Generate the first five terms of a non-linear sequence by substituting `n = 1, 2, 3, 4, 5` into the given nth term formula.
  • Find any term in a non-linear sequence by substituting the required value of `n` into the nth term formula.


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