6 P61186A 5. An increasing sequence {un} for n  ` is such that the difference between the nth term of {un} and the mean of the previous two terms of {un} is always 6 (a) Show that, for n . 3 2un – un – 1 – un – 2 = 12 (2) Given that u1 = 2 and u2 = 8 (b) find the solution of this second order recurrence relation to obtain an expression for un in terms of n. (7) (c) Show that as n o ’, un o kn where k is a constant to be determined. You must give reasons for your answer. (2) (Total for Question 5 is 11 marks) 7 P61186A Turn over 6. B H C2 C2 C1 C1 D E F C G A S T (3, 6) (5, 7) (4, 7) (5, 8) (6, 8) (5, 6) (4, 7) (17, 20) (10, 12) (10, 14) (2, 4) (13, 17) (8, 11) (7, 9) (0, 4) (3, 5) (3, 5) (1, 2) (4, 4) (3, 5) Figure 2 Figure 2 shows a capacitated, directed network. The network represents a system of pipes through which fluid flows from a source, S, to a sink, T. The numbers (l, u) on each arc represent, in litres per second, the lower capacity, l, and the upper capacity, u, of the corresponding pipe. Two cuts C1 and C2 are shown. (a) Find the capacity of (i) cut C1 (ii) cut C2 (2) (b) Explain why the arcs AE and CE cannot be at their upper capacities simultaneously. (1) (c) Explain why a flow of 31 litres per second through the system is not possible. (1) (d) Hence determine a minimum feasible flow and a maximum feasible flow through the system. You must draw these feasible flows on the diagrams in the answer book and give reasons to justify your answer. You should not apply the labelling procedure to find these flows. (4) (Total for Question 6 is 8 marks)