Consider the following sequence of numbers, where the dependent variable is P (n) and
the independent variable is n.
1 2 6 16 44 120
1. Formulate a second order ordinary difference equation that describes the sequence
of numbers presented. Show all workings by answering the following questions:
i. State the five equations that clearly indicate changes in each discrete time
interval resulting in the data provided.
(Hint: write equations for P (2),P (3), P (4), P (5)) (2)
ii. After recognising a pattern in i. , write a second order ordinary difference
equation that describes the specified problem where the first two numbers in
the sequence are initial conditions P (0) = 1 and P (1) = 2. (1)
2. Solve the appropriate ordinary difference equation subject to the correct initial
conditions. (4)
3. Calculate P (12). (1)
4. After how many discrete time intervals will P(n)=423324672?
