11864 12 (a) (i) Prove that the sum of n terms of an arithmetic progression with first term a and last term l is Sn = 1 2 n(a + l) [4] [Turn over 11864 The first term of an arithmetic progression is 7 and the last term is 79 The sum of the progression is 1075 (ii) Find the number of terms. [3] (iii) Find the common difference. [3] 11864 (b) A salesman receives a bonus at the end of each year and decides to invest this money in a savings account. At the end of Year 1 he invests £400 At the end of Year 2 he invests a further £400 and receives 2% interest on the first year’s £400 At the end of Year 3 he invests a further £400 and 2% interest is added to the total sum of money which he has accumulated during the first two years. (i) Show that he has £1,224.16 in his account at the end of Year 3 [4] [Turn over 11864 (ii) Assuming that the man continues to invest in this way, form and sum a series to prove that he will have £20 000(1.02n − 1) in his account at the end of n years. [6] 11864 (iii) Hence find the least number of years until his investment exceeds £7,000 [4] THIS IS THE END OF THE QUESTION PAPER 11864 BLANK PAGE DO NOT WRITE ON THIS PAGE Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright holders may have been unsuccessful and CCEA will be happy to rectify any omissions of acknowledgement in future if notified. Examiner Number DO NOT WRITE ON THIS PAGE 11864/4 For Examiner’s use only Question Number Marks 1 2 3 4 5 6 7 8 9 10 11 12 Total Marks