Understand and use the binomial expansion of \((a + bx)^n\) for positive integer \(n\); the notations \(n!\), \(nCr\) and \(\binom{n}{r}\); link to binomial probabilities.

Extend to any rational \(n\), including its use for approximation; be aware that the expansion is valid for \(|\frac{bx}{a}| < 1.\) (Proof not required.)

Factorials and combinations Binomial expansion Advanced binomial expansion

Work with sequences including those given by a formula for the nth term and those generated by a simple relation of the form \(x_{n+1} = f(x_n)\); increasing sequences; decreasing sequences; periodic sequences.

Sequences

Understand and use sigma notation for sums of series.

Sigma notation

Understand and work with arithmetic sequences and series, including the formulae for \(n\)th term and the sum to \(n\) terms.

Arithmetic sequences and series

Understand and work with geometric sequences and series including the formulae for the \(n\)th term and the sum of a finite geometric series; the sum to infinity of a convergent geometric series, including the use of \(|r| < 1\); modulus notation.

Geometric sequences and series

Use sequences and series in modelling.

Arithmetic sequences and series Geometric sequences and series