Sequences and recurrence relationsEdexcel International A Level Maths: Mind map

Exam questions on Sequences and recurrence relations

1. A sequence is given by $u_n=n^2-6n+10$ for $n\ge1$.
   Find an expression for $u_{n+1}-u_n$ in terms of $n$, and hence state the values of $n$ for which $u_{n+1}>u_n$.2 marks
2. A sequence is defined by $u_1=2$ and $u_{n+1}=\dfrac{1}{1-u_n}$ for $n\ge1$.
   Find the value of $u_{100}$.2 marks
3. A sequence has $n$th term $u_n=a+b(-1)^n$, where $a$ and $b$ are constants, $u_1=3$ and $u_2=9$.
   Find the values of $a$ and $b$.3 marks