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

Exam questions on Second-order recurrence relations

1. A sequence satisfies $u_{n+2}=5u_{n+1}-6u_n$ with $u_1=5$ and $u_2=13$.
   Find $u_n$ in terms of $n$.2 marks
2. A sequence satisfies $u_{n+2}=6u_{n+1}-9u_n$ with $u_1=3$ and $u_2=18$.
   Find $u_n$ in terms of $n$.2 marks
3. A sequence satisfies $u_{n+2}-u_{n+1}-6u_n=12$ with $u_1=2$ and $u_2=20$.
   Find the complementary function and a particular solution of the form $u_n=\lambda$.3 marks