Sequences, recurrence relations and sigma notationEdexcel A-Level Maths: Mind map

Exam questions on Sequences, recurrence relations and sigma notation

1. A sequence is defined by $u_1=5$ and $u_{n+1}=2u_n-3$ for $n\ge1$.
   Calculate $\sum_{r=1}^{4}u_r$.2 marks
2. A sequence is defined by $u_1=2$ and $u_{n+1}=\frac{8}{u_n}$ for $n\ge1$.
   Explain why the sequence is periodic and state its order.2 marks
3. A sequence has $n$th term $u_n=n^2-8n+20$ for $n\ge1$.
   Show that $u_{n+1}-u_n=2n-7$, and hence find the values of $n$ for which $u_{n+1}<u_n$.3 marks