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This homework assignment focuses on analyzing recurrence relations in mathematical sequences. Students will work with the sequences defined by un+1 = 1.1un + 3 (with u0 = 5) and vn+1 = 0.7vn + 10 (with v0 = 5), finding the first five terms and discussing their limiting behavior. Additionally, they will address a debt scenario where a loan of £2000 incurs a monthly repayment of 30% of the outstanding balance, while also borrowing an additional £250 each month. The assignment requires setting up a recurrence relation for the outstanding balance and analyzing debt management.
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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
