Generate a sequence by spotting a pattern or using a term-to-term rule given algebraically or in words.

e.g.  Continue the sequences
1, 4, 7, 10, ...

1, 4, 9, 16, ...

Find a position-to-term rule for simple arithmetic sequences, algebraically or in words.

e.g.  2, 4, 6, ... \(2n\)

3, 4, 5, ... \(n + 2\)

Generate a sequence from a formula for the nth term.

e.g. nth term \(= n^2+2n\) gives 3, 8, 15, ...

Find a formula for the nth term of an arithmetic sequence.

e.g.  40, 37, 34, 31, ... \(43 - 3n\)

Use subscript notation for position-to-term and term-to-term rules.

e.g. \(x_n = n+2\)

\(x_{n+1} = 2x_n - 3\)

Find a formula for the nth term of a quadratic sequence.

e.g.  0, 3, 10, 21, ...
\(u_n = 2n^2 - 3n + 1\)

Recognise sequences of triangular, square and cube numbers, and simple arithmetic progressions.

Recognise Fibonacci and quadratic sequences, and simple geometric progressions (\(r^n\) where \(n\) is an integer and \(r\) is a rational number \(> 0\)).

Generate and find nth terms of other sequences.

e.g. \(1, \sqrt{2}, 2, 2\sqrt{2}, ...\)

\(\dfrac{1}{2}, \dfrac{2}{3}, \dfrac{3}{4}, ... \)