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

Exam questions on First-order recurrence relations

1. A sequence is defined by $u_{n+1}-5u_n=8$ for $n\geq1$, with $u_1=1$.
   Hence find $u_n$ in terms of $n$.2 marks
2. A fish farm models the number of fish $P_n$ in a lake at the start of year $n$ by $P_{n+1}=1.15P_n-60$, with $P_1=500$. Each year the population grows by 15% and then 60 fish are removed.
   Given that $P_n=100(1.15)^{n-1}+400$, find the first year in which the population exceeds $1000$.2 marks
3. A sequence satisfies $u_{n+1}-2u_n=6n$ for $n\geq1$, with $u_1=5$.
   Find the complementary function and a particular solution of the form $u_n=an+b$.3 marks