A-Level Maths Edexcel (9MA0)

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

For example

• $u_n = \dfrac{1}{3n+1}$ describes a decreasing sequence as $u_n + 1 < u_n$ for all integer $n$
• $u_n = 2^n$ is an increasing sequence as $u_n + 1 > u_n$ for all integer $n$
• $u_{n+1} = \dfrac{1}{u_n}$ for $n > 1$ and $u_1 = 3$ describes a periodic sequence of order 2