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Higher Maths Homework

Unit 1. Higher Maths Homework. Recurrence relations. 1. Given u n+1 = 1.1 u n + 3 u 0 = 5 and v n+1 = 0.7 v n + 10 v 0 = 5 a) Find the first 5 terms of each sequence.

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Higher Maths Homework

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  1. Unit 1 Higher Maths Homework Recurrence relations 1.Given un+1 = 1.1 un+ 3 u0 = 5 and vn+1 = 0.7 vn+ 10 v0 = 5 a) Find the first 5 terms of each sequence. b) Explain why one sequence tends to a limit as n tends to infinity and the other doesn’t. c) For the one that tends to a limit, calculate that limit. 6 2.For the recurrence relation vn+1 = avn+ b v1 = 2, v2 = 9 and v3 = 51 Find a , b and v5. . 6 3.On the 1st March I borrowed £2000 from a (good) friend who decided not to charge me any interest. On the 25th of each month, I pay back 30% of the outstanding balance, but unfortunately have to approach my friend on the last day of each month to borrow a further £250. a) How much do I owe on 1st April, 1st May and 1st June? b) Set up a recurrence relation to show the outstanding balance Bn due at the beginning of each month. c) Will I ever clear my debts, if I carry on like this? If not explain what will eventually happen 6 Total 18 marks

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