Sequences and Series

AS Level

  • Understand and use the binomial expansion of (a+bx)n for positive integer n; the notations n! and nCr; link to binomial probabilities

A Level

  • Extend to any rational n, including its use for approximation; be aware of when the expansion is valid

  • Work with sequences including those given by a formula for the nth term and those generated by a simple relation of the form xn+1 = f(xn); 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 nth term and the sum to n terms

  • Understand and work with geometric sequences and series including the formulae for the nth 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