Second-order recurrence relationsEdexcel A-Level Further Maths: Mind map

Exam questions on Second-order recurrence relations

1. A sequence satisfies $u_{n+2}-7u_{n+1}+12u_n=0$ for $n\geq1$, with $u_1=2$ and $u_2=2$.
   Find $u_n$ in terms of $n$.2 marks
2. A sequence satisfies $u_{n+2}-6u_{n+1}+9u_n=16$ for $n\geq1$, with $u_1=10$ and $u_2=31$.
   Find $u_n$ in terms of $n$.2 marks
3. A sequence satisfies $u_{n+2}-5u_{n+1}+6u_n=2n+1$ for $n\geq1$, with $u_1=8$ and $u_2=17$.
   Find a particular solution of the form $u_n=an+b$.3 marks