1. Topic Past Papers –Seq & Series 1AH
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 …+ 56.
b) A geometric sequence of positive terms has first term 2, and the sum of the first three terms
is 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

2. Topic Past Papers –Seq & Series 1AH
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

3. Topic Past Papers –Seq & Series 1AH
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

4. Topic Past Papers –Seq & Series 1AH
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) 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) q – 12q c) Proof
2008
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