Sequences and recurrence relationsAQA A-Level Maths: Mind map

Exam questions on Sequences and recurrence relations

1. A sequence is defined by $u_1=3$ and $u_{n+1}=2u_n-1$ for $n\ge1$.
   Show that $u_n=2^n+1$ satisfies both $u_1=3$ and the relation $u_{n+1}=2u_n-1$.2 marks
2. A sequence has $n$th term $a_n=\frac{n}{n+2}$ for $n\ge1$.
   Prove that the sequence is increasing.2 marks
3. A sequence is defined by $x_1=2$ and $x_{n+1}=\frac{1}{1-x_n}$ for $n\ge1$.
   Find $x_2$, $x_3$ and $x_4$, and state what this shows about the sequence.3 marks