Compiled by Navan Mudali Sequences & Series - Past Questions & Solutions November 2008 Page 1 of 103 Compiled by Navan Mudali Page 2 of 103 Compiled by Navan Mudali Page 3 of 103 Compiled by Navan Mudali Page 4 of 103 Compiled by Navan Mudali Page 5 of 103 Compiled by Navan Mudali Page 6 of 103 Compiled by Navan Mudali November 2009 Page 7 of 103 Compiled by Navan Mudali Page 8 of 103 Compiled by Navan Mudali Page 9 of 103 Compiled by Navan Mudali Page 10 of 103 Compiled by Navan Mudali Page 11 of 103 Compiled by Navan Mudali Page 12 of 103 Compiled by Navan Mudali Page 13 of 103 Compiled by Navan Mudali Page 14 of 103 Compiled by Navan Mudali February 2010 Page 15 of 103 Compiled by Navan Mudali Page 16 of 103 Compiled by Navan Mudali Page 17 of 103 Compiled by Navan Mudali Page 18 of 103 Compiled by Navan Mudali Page 19 of 103 Compiled by Navan Mudali November 2010 Page 20 of 103 Compiled by Navan Mudali Page 21 of 103 Compiled by Navan Mudali Page 22 of 103 Compiled by Navan Mudali Page 23 of 103 Compiled by Navan Mudali Page 24 of 103 Compiled by Navan Mudali February 2011 QUESTION 2 The sequence 3 ; 9 ; 17 ; 27 ; … is a quadratic sequence. 2.1 2.2 2.3 Write down the next term. th Determine an expression for the n term of the sequence. What is the value of the first term of the sequence that is greater than 269? (1) (4) (4) [9] QUESTION 3 3.1 The first two terms of an infinite geometric sequence are 8 and 8 . Prove, without the use 2 of a calculator, that the sum of the series to infinity is 3.2 16 8 2 . (4) The following geometric series is given: x = 5 + 15 + 45 + … to 20 terms. 3.2.1 3.2.2 Write the series in sigma notation. Calculate the value of x. (2) (3) [9] QUESTION 4 4.1 The sum to n terms of a sequence of numbers is given as: 4.1.1 4.1.2 4.2 Sn n 5n 9 2 Calculate the sum to 23 terms of the sequence. Hence calculate the 23rd term of the sequence. (2) (3) The first two terms of a geometric sequence and an arithmetic sequence are the same. The first term is 12. The sum of the first three terms of the geometric sequence is 3 more than the sum of the first three terms of the arithmetic sequence. Determine TWO possible values for the common ratio, r, of the geometric sequence. (6) [11] Page 25 of 103 Compiled by Navan Mudali Page 26 of 103 Compiled by Navan Mudali Page 27 of 103 Compiled by Navan Mudali Page 28 of 103 Compiled by Navan Mudali Page 29 of 103 Compiled by Navan Mudali November 2011 Page 30 of 103 Compiled by Navan Mudali Page 31 of 103 Compiled by Navan Mudali Page 32 of 103 Compiled by Navan Mudali Page 33 of 103 Compiled by Navan Mudali Page 34 of 103 Compiled by Navan Mudali Page 35 of 103 Compiled by Navan Mudali Page 36 of 103 Compiled by Navan Mudali February 2012 Page 37 of 103 Compiled by Navan Mudali Page 38 of 103 Compiled by Navan Mudali Page 39 of 103 Compiled by Navan Mudali Page 40 of 103 Compiled by Navan Mudali Page 41 of 103 Compiled by Navan Mudali Page 42 of 103 Compiled by Navan Mudali Page 43 of 103 Compiled by Navan Mudali November 2012 Page 44 of 103 Compiled by Navan Mudali Page 45 of 103 Compiled by Navan Mudali Page 46 of 103 Compiled by Navan Mudali Page 47 of 103 Compiled by Navan Mudali Page 48 of 103 Compiled by Navan Mudali Page 49 of 103 Compiled by Navan Mudali Page 50 of 103 Compiled by Navan Mudali Page 51 of 103 Compiled by Navan Mudali February 2013 Page 52 of 103 Compiled by Navan Mudali Page 53 of 103 Compiled by Navan Mudali Page 54 of 103 Compiled by Navan Mudali Page 55 of 103 Compiled by Navan Mudali Page 56 of 103 Compiled by Navan Mudali Page 57 of 103 Compiled by Navan Mudali November 2013 Page 58 of 103 Compiled by Navan Mudali Page 59 of 103 Compiled by Navan Mudali Page 60 of 103 Compiled by Navan Mudali Page 61 of 103 Compiled by Navan Mudali Page 62 of 103 Compiled by Navan Mudali February 2014 Page 63 of 103 Compiled by Navan Mudali Page 64 of 103 Compiled by Navan Mudali Page 65 of 103 Compiled by Navan Mudali Page 66 of 103 Compiled by Navan Mudali Page 67 of 103 Compiled by Navan Mudali Page 68 of 103 Compiled by Navan Mudali November 2014 Page 69 of 103 Compiled by Navan Mudali Page 70 of 103 Compiled by Navan Mudali Page 71 of 103 Compiled by Navan Mudali Page 72 of 103 Compiled by Navan Mudali Page 73 of 103 Compiled by Navan Mudali Page 74 of 103 Compiled by Navan Mudali Page 75 of 103 Compiled by Navan Mudali November 2014 Exemplar Page 76 of 103 Compiled by Navan Mudali Page 77 of 103 Compiled by Navan Mudali Page 78 of 103 Compiled by Navan Mudali Page 79 of 103 Compiled by Navan Mudali Page 80 of 103 Compiled by Navan Mudali February 2015 Page 81 of 103 Compiled by Navan Mudali Page 82 of 103 Compiled by Navan Mudali Page 83 of 103 Compiled by Navan Mudali Page 84 of 103 Compiled by Navan Mudali Page 85 of 103 Compiled by Navan Mudali November 2015 Page 86 of 103 Compiled by Navan Mudali Page 87 of 103 Compiled by Navan Mudali Page 88 of 103 Compiled by Navan Mudali Page 89 of 103 Compiled by Navan Mudali Page 90 of 103 Compiled by Navan Mudali March 2016 Page 91 of 103 Compiled by Navan Mudali Page 92 of 103 Compiled by Navan Mudali Page 93 of 103 Compiled by Navan Mudali Page 94 of 103 Compiled by Navan Mudali Page 95 of 103 Compiled by Navan Mudali Page 96 of 103 Compiled by Navan Mudali Page 97 of 103 Compiled by Navan Mudali November 2016 Page 98 of 103 Compiled by Navan Mudali Page 99 of 103 Compiled by Navan Mudali Page 100 of 103 Compiled by Navan Mudali Page 101 of 103 Compiled by Navan Mudali Page 102 of 103 Compiled by Navan Mudali Page 103 of 103
