Homework 5 on Sequences and Business Arithmetic Part 2 Your Score: Q1) The first five terms of an arithmetic sequence are: 1 2 3 4 5 234 228 222 216 210 What is the nth term formula? n + After how many terms will the sequence be less than -500 ? Q2) Term 7 of an arithmetic sequence is: 39 Term 20 of the same sequence is: 130 Find the first term and the common difference: a = d = Q3) An arithmetic progression has a first term of -30 and a common difference of 3 Find the sum of the first 500 terms. Sum = Q4) Term 21 of an Arithmetic Progression is 122 The sum of the first 39 terms of the same progression is 4512.3 Find the first term and the common difference. a = d = Q5) Find term 12 of the following sequence: 0.2 0.5 1.25 3.125 7.8125 . . . . . Q6) Term 6 of a geometric sequence is -2048 Term 3 the same sequence is -32 Find the first term and the value of the ratio. a = r1 = List the first five terms of the sequence below: Q7) If possible, find the sum to infinity of the following series. If the series is divergent, enter "d". a) 3 1.2 0.48 0.192 0.0768 Sinf = b) 3 4.2 5.88 8.232 11.5248 Sinf = c) 3 -1.2 0.48 -0.192 0.0768 Sinf = Q8) Term 4 of a geometric sequence is 13.5 Term 2 the same sequence is 24 Find the sum to infinity of this series: a = r = S = Q9) You're saving up for a boat which costs £240,000 You deposit £23,400 at the start of each year into an account. The account pays compound interest at 3.100% paid at the end of each year. a) What is the value of the investment at the end of year 6 b) How long will it take to save up for the boat? years Challenge Question Q10) The mortgage on a house is £468,000 The bank charges 0.210% on the outstanding debt each month. The monthly repayments are £2,600.00 How many month will it take to repay the loan? months years