A-Level Maths AQA 7357

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.)

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.

Understand and use sigma notation for sums of series.

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

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.

Use sequences and series in modelling.