Topic Past Papers –Seq & Series 1 AH Topic Past Papers –Seq & Series 1 Unit 2 Outcome 4 2002 A10. Define Sn (x) by where n is a positive integer. Express Sn (1) in terms of n. By considering (1 – x) Sn (x), show that Obtain the value of 2 marks 4 marks 3 marks 2003 A2. 3 marks 2 marks 2004 16. a) Obtain the sum of the series 8 + 11 + 14 + …+ 56. b) A geometric sequence of positive terms has first term 2, and the sum of the first three terms is 266. Calculate the common ratio. c) An arithmetic sequence, A has first term a and common difference 2, and a geometric sequence, B, has first term a and common ratio 2. The first four terms of each sequence have the same sum. Obtain the value of a. Obtain the smallest value of n such that the sum to n terms for sequence B is more than twice the sum to n terms for sequence A. 2 marks 3 marks 3 marks 2 marks 2005 4. The sum S(n), of the first n terms of a sequence, u1, u2, u3, … is given by S(n)= 8n – n2, n ≥ 1. Calculate the values of u1, u2, u3 and state what type of sequence it is. Obtain a formula for un in terms of n, simplifying your answer. 3 marks 2 marks 2006 16. The first three terms of a geometric sequence are (a) Obtain expressions for the common ratio and the nth term of the sequence. (b) Find an expression for the sum of the first n terms of the sequence. (c) Obtain the range of values of x for which the sequence has a sum to infinity and find an expression for the sum to infinity. 3 marks 3 marks 4 marks Lanark Grammar Mathematics Department Mrs Leck

Topic Past Papers –Seq & Series 1 AH Topic Past Papers –Seq & Series 1 Unit 2 Outcome 4 2007 9. Show that Hence write down a formula for 2 marks 1 mark 2 marks 2008 1. The first term of an arithmetic sequence is 2 and the 20th term is 97. Obtain the sum of the first 50 terms. 4 marks 2009 12. The first two terms of a geometric sequence are a1 = p and a2 = p2. Obtain expressions for Snand S2n, in terms of p, where Given that S2n = 65Sn show that pn = 64. Given also that a3 = 2p and that p > 0, obtain the exact value of p and hence the value of n. 1, 1 marks 2 marks 1, 1 marks 2010 2. The second and third terms of a geometric series are -6 and 3 respectively. Explain why the series has a sum to infinity, and obtain this sum. 5 marks 2011 8. Write down an expression for and an expression for 1 mark 3 marks 2012 2. The first and fourth terms of a geometric series are 2048 and 256 respectively. Calculate the value of the common ratio. Given that the sum of the first n terms is 4088, find the value of n. 2 marks 3 marks Lanark Grammar Mathematics Department Mrs Leck

Topic Past Papers –Seq & Series 1 AH Topic Past Papers –Seq & Series 1 Unit 2 Outcome 4 2013 17. Write down the sums to infinity of the geometric series and valid for Assuming that it is permitted to integrate an inifinite series term by term, show that, for Show how this series can be used to evaluate ln2. Hence determine the value of ln2 correct to 3 decimal places. 7 marks 3 marks 2014 14. (a) Given the series write down the sum to infinity when Hence obtain an infinite geometric series for For what values of r is this series valid? Express in partial fractions. Hence, or otherwise, determine the first three terms of an infinite series for For what values of r does the series converge? 4 marks 6 marks Lanark Grammar Mathematics Department Mrs Leck

Topic Past Papers –Seq & Series 1 AH Topic Past Papers –Seq & Series 1 Unit 2 Outcome 4 2002 A10. 2003 A2 a) or b) n = 3 and 7. (3) (2) 2004 16. a) 544 b) r = 11 c) smallest n is 7 2005 4. a) b) 9 – 2n (3) (2) 2006 (3) (3) (4) 2007 9.a) Proof b) 2q – 12q2 c) Proof 2008 1. 6225 2009 12.a) b) Proof c) (2) (2) (2) 2010 2. Sum to infinity as r = - ½ Sum to infinity = 8. 2011 8. 2012 2. (5) 2013 2014 14. 17. (4, 6) (4, 3, 3) (7, 3) Lanark Grammar Mathematics Department Mrs Leck