5. (a) Consider the following sequence of equations. 1 x 2 = 3 (1 x2 x 3), 1 x 2+2 x3= 3 (2 x3 x4), 1 x 2+2 x3+3 x4 = 3 (3 x4 x 5), (i) Formulate a conjecture for the " equation in the sequence. (ii) Verify your conjecture for n = 4. (2) (b) A sequence of numbers has the "" term given by un = 2"+3.n E Z*. Bill conjectures that all members of the sequence are prime numbers. Show that Bill's conjecture is false. (2) (c) Use mathematical induction to prove that 5 x 7" + 1 is divisible by 6 for all n E Z+. (6)