Sequences — Paper 1 · IGCSE Mathematics 0580

16 Look at the sequence of numbers 7, 11, 15, 19, ………. (a) Write down the next number in the sequence. Answer (a) [1] (b) Find the 10th number in the sequence. Answer (b) [1] (c) Write an expression, in terms of n, for the nth number in the sequence. Answer (c) [1]

3 marks

Mark scheme: 16 (a) 23 isw 1 ignore extras even if incorrect (b) 43 1ft their (a) + 20 (c) 4n + 3 oe final answer 1 allow any unsimplified form 14 e.g. 7 + (n – 1) × 4 or 7 + 4n – 4 IGCSE – JUNE 2005 0580/0581 1

This question in 0580/11 May/June 2005

4 The nth term of a sequence is given by n2+2. Work out the 4th term. Answer [1]

1 marks

Mark scheme: 4 18 1

This question in 0580/11 Oct/Nov 2006

2 Write down the next term in each sequence. (a) 1, 2, 4, 8, 16, [1] (b) 23, 19, 15, 11, 7, [1]

2 marks

Mark scheme: 2 (a) 32 1 (b) 3 1

This question in 0580/13 May/June 2011

10 Here are the fi rst four terms of a sequence. 4 11 18 25 Write down an expression for the nth term. Answer … [2] _____________________________________________________________________________________

2 marks

Mark scheme: 10 7n − 3 oe 2 B1 for 7n

This question in 0580/11 May/June 2013

8 For Examiner's Use 1 row 2 rows 3 rows Complete the table for 4 rows and 5 rows. Number of rows 1 2 3 4 5 Number of cans 1 3 6 [2] _____________________________________________________________________________________

2 marks

Mark scheme: 8 10, 15 1, 1 If 10 not correct allow SC1 for x, x + 5

This question in 0580/12 May/June 2013

23 (a) Here are the fi rst four terms of a sequence. For Examiner′s Use 27 23 19 15 (i) Write down the next term in the sequence. Answer(a)(i) … [1] (ii) Explain how you worked out your answer to part (a)(i). Answer(a)(ii) … [1] (b) The nth term of a different sequence is 4n – 2 . Write down the fi rst three terms of this sequence. Answer(b) … , … , … [1] (c) Here are the fi rst four terms of another sequence. –1 2 5 8 Write down the nth term of this sequence. Answer(c) … [2] _____________________________________________________________________________________

5 marks

Mark scheme: 23 (a) (i) 11 1 (ii) subtract 4 oe 1 (b) 2, 6, 10 cao 1 (c) 3n – 4 oe 2 B1 for answer 3n ± k, where k is an integer

This question in 0580/11 Oct/Nov 2013

20 (a) 2, 3, 6, 11, 18, . . . (i) Write down the next two terms in this sequence. Answer(a)(i) … , … [2] (ii) Describe, in words, the rule for continuing this sequence. Answer(a)(ii) … [1] (b) The nth term of a different sequence is 4n – 3. Work out the first three terms in this sequence. Answer(b) … , … , … [1] __________________________________________________________________________________________

4 marks

Mark scheme: 20 (a) (i) 27, 38 2 B1 for 27 and B1FT for their 27 + 11 (ii) Add the next odd number oe 1 (b) 1, 5, 9 1

This question in 0580/11 May/June 2015

22 (a) Write down the next term in each of these sequences. (i) 5 9 13 17 . . . Answer(a)(i) … [1] (ii) 3 6 12 24 . . . Answer(a)(ii) … [1] (b) Here are the first four terms in a different sequence. 2 7 12 17 Find an expression for the nth term of this sequence. Answer(b) … [2] __________________________________________________________________________________________

4 marks

Mark scheme: 22 (a) (i) 21 1 (ii) 48 1 (b) 5n – 3 oe final answer 2 B1 for 5n + a or bn – 3 (b ≠ 0)

This question in 0580/11 Oct/Nov 2015

9 –1, 3, 7, 11, … Write down the nth term for this sequence. Answer … [2]

2 marks

Mark scheme: 9 4n − 5 oe 2 M1 for 4n + k or for jn −5 (j≠0) 14 5

This question in 0580/12 Oct/Nov 2015

8 These are the first four terms in a sequence. 21 17 13 9 (a) Write down the next number in this sequence. Answer(a) … [1] (b) Write down the rule for continuing the sequence. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 8 (a) 5 1 (b) Subtract 4 oe 1

This question in 0580/13 Oct/Nov 2015

20 35, 41, 47, 53, 59, … For this sequence, write down (a) the next term, … [1] (b) the nth term. … [2]

3 marks

Mark scheme: 20 (a) 65 1 (b) 6n + 29 oe 2 M1 for 6n + c or kn + 29, k≠0 ( ) ( 2 ) ( )

This question in 0580/12 Feb/March 2016

17 Find the next term in each of these sequences. (a) 3, 7, 11, 15, … … [1] (b) 10, 7, 4, 1, … … [1] (c) 1, 9, 25, 49, … … [1]

3 marks

Mark scheme: 17 (a) 19 1 (b) −2 1 (c) 81 1

This question in 0580/11 May/June 2016

9 Here are the first five terms in a sequence. 4 11 18 25 32 Find an expression for the nth term of this sequence. … [2]

2 marks

Mark scheme: 9 7n – 3 oe 2 M1 for 7n + a or bn – 3 (b ≠ 0)

This question in 0580/12 May/June 2016

15 Write down the next term in each of these sequences. (a) 19, 15, 11, 7, 3, … [1] (b) 0, 1, 4, 9, 16, … [1] (c) 3, 5, 9, 17, 33, … [1]

3 marks

Mark scheme: 15 (a) –1 1 (b) 25 1 (c) 65 1

This question in 0580/12 Feb/March 2017

7 (a) Write down the next term in this sequence. 24, 22, 18, 12, 4, … … [1] (b) The nth term of another sequence is 3n + 5. Write down the first three terms in this sequence. … , … , … [1]

2 marks

Mark scheme: 7(a) −6 1 7(b) 8, 11, 14 1

This question in 0580/13 May/June 2017

22 (a) These are the first four terms of a sequence. 8 15 22 29 (i) Write down the next term. … [1] (ii) Write down the rule for continuing the sequence. … [1] (b) These are the first four terms of a different sequence. 2 6 10 14 Find an expression for the nth term of this sequence. … [2]

4 marks

Mark scheme: 22(a)(i) 36 1 22(a)(ii) Add 7 oe 1 22(b) 4n – 2 oe 2 M1 for 4n + k, k ≠ −2 oe

This question in 0580/12 Oct/Nov 2017

20 (a) These are the first five terms of a sequence. 4 10 16 22 28 (i) Write down the next term. … [1] (ii) Write down the rule for continuing the sequence. … [1] (b) These are the first five terms of a different sequence. 11 14 17 20 23 Find an expression for the nth term of this sequence. … [2]

4 marks

Mark scheme: 20(a)(i) 34 1 20(a)(ii) Add 6 oe 1 20(b) 3n + 8 oe 2 B1 for 3n + k

This question in 0580/13 Oct/Nov 2017

4 The nth term of a sequence is 5n - 3. Write down the first three terms of the sequence. … , … , … [1]

1 marks

Mark scheme: 4 2 7 12 cao 1

This question in 0580/11 May/June 2018

6 Here is a sequence. a, 13, 9, 3, –5, –15, b, … Find the value of a and the value of b. a = … b = … [2]

2 marks

Mark scheme: 6 [a =]15 2 B1 for each [b =] −27 or SC1 for reversed answers

This question in 0580/12 May/June 2018

19 These are the first five terms in a sequence. 8 11 14 17 20 (a) Find the next term. … [1] (b) Find an expression for the nth term. … [2]

3 marks

Mark scheme: 19(a) 23 1 19(b) 3n + 5 oe 2 B1 for 3n + j or kn + 5, k ≠ 0

This question in 0580/11 Oct/Nov 2018

14 (a) The expression for the nth term of a sequence is 5n 2. Work out the third term in this sequence. … [1] (b) These are the first five terms of a sequence. - 4 2 8 14 20 Find an expression for the nth term of this sequence. … [2]

3 marks

Mark scheme: 14(a) 45 1 14(b) 6n – 10 oe 2 B1 for 6n + c or kn – 10 (k ≠ 0)

This question in 0580/12 Oct/Nov 2018

16 These are the first four terms of a sequence. 5 8 11 14 (a) Write down the next term. … [1] (b) Find an expression, in terms of n, for the nth term. … [2]

3 marks

Mark scheme: 16(a) 17 1 16(b) 3n + 2 oe final answer 2 B1 for 3n + k or cn + 2, c≠ 0

This question in 0580/11 May/June 2019

21 (a) Write down the next term in each sequence. (i) 12, 7, 2, -3, -8, … [1] (ii) 4, 7, 13, 25, 49, … [1] (b) Find an expression, in terms of n, for the nth term of this sequence. 5, 8, 11, 14, … … [2]

4 marks

Mark scheme: 21(a)(i) −13 1 21(a)(ii) 97 1 21(b) 3n + 2 oe final answer 2 B1 for 3n + j or kn + 2 k ≠ 0

This question in 0580/13 May/June 2019

12 (a) The nth term of a sequence is 60 - 8n . Find the largest number in this sequence. … [1] (b) Here are the first five terms of a different sequence. 12 19 26 33 40 Find an expression for the nth term of this sequence. … [2]

3 marks

Mark scheme: 12(a) 52 1 12(b) 7n + 5 oe final answer 2 B1 for 7n + a or bn + 5 b ≠ 0

This question in 0580/11 May/June 2020

14 These are the first four terms of a sequence. 17 10 3 - 4 (a) (i) Find the next term. … [1] (ii) Write down the term to term rule for continuing this sequence. … [1] (b) These are the first four terms of a different sequence. - 2 2 6 10 Find an expression for the nth term. … [2]

4 marks

Mark scheme: 14(a)(i) –11 1 14(a)(ii) Subtract 7 1 14(b) 4n – 6 oe final answer 2 B1 for 4n + j or kn – 6 k ≠ 0

This question in 0580/12 Oct/Nov 2020

14 These are the first four terms of a sequence. 29 22 15 8 (a) Write down the next two terms. … , … [2] (b) Find the nth term. … [2]

4 marks

Mark scheme: 14(a) 1 −6 2 B1 for each If 0 scored, SC1 for two terms with a difference of −7 14(b) 36 − 7n oe final answer 2 B1 for 36 + jn , j ≠ 0 or k − 7n or for correct answer shown in working and then spoilt

This question in 0580/12 Feb/March 2021

12 The nth term of a sequence is 6n - 4 . (a) Write down the first 3 terms in this sequence. … , … , … [1] (b) The kth term of this sequence is 422. Work out the value of k. k = … [2]

3 marks

Mark scheme: 12(a) 2 8 14 1 12(b) 71 2 M1 for 6k – 4 = 422 or better

This question in 0580/11 May/June 2021

17 These are the first four terms of a sequence. 7 11 15 19 Find the nth term. … [2]

2 marks

Mark scheme: 17 4n + 3 oe 2 B1 for 4n + j or kn + 3 (k ≠ 0) as answer or 4n + 3 oe seen then spoilt

This question in 0580/13 May/June 2021

12 (a) 7, 13, 19, 25, … Find the next term in this sequence. … [1] (b) 30, 26, 22, 18, … Write down the term to term rule for this sequence. … [1] (c) -1, 1, 3, 5, … Find the nth term for this sequence. … [2]

4 marks

Mark scheme: 12(a) 31 1 12(b) Subtract 4 oe 1 12(c) 2n – 3 oe final answer 2 B1 for 2n + c or kn – 3 (k ≠ 0) or for 2n – 3 oe spoilt or –1 + 2(n – 1) spoilt

This question in 0580/11 Oct/Nov 2021

17 These are the first four terms of a sequence. 3 10 17 24 (a) Write down the next term. … [1] (b) Write down the term to term rule. … [1] (c) Find the nth term. … [2] (d) Find the 40th term. … [2]

6 marks

Mark scheme: 17(a) 31 1 17(b) + 7 oe 1 17(c) 7n – 4 oe 2 B1 for 7n + b or an – 4 (a ≠ 0) or for a correct answer (including unsimplified) shown in the working but spoilt 17(d) 276 2 FT their (c) M1 for their ax + b

This question in 0580/12 Oct/Nov 2021

14 (a) These are the first four terms of a sequence. 17 23 29 35 Find the next term. … [1] (b) These are the first four terms of a different sequence. 3 -1 -5 -9 (i) Find the next term in this sequence. … [1] (ii) Find the nth term. … [2]

4 marks

Mark scheme: 14(a) 41 1 14(b)(i) –13 1 14(b)(ii) –4n + 7 oe final answer 2 B1 for –4n + k or jn + 7 (j ≠ 0) or for a correct answer spoilt

This question in 0580/13 Oct/Nov 2021

18 These are the first four terms of a sequence. 1 23 45 67 (a) Write down the next two terms. … , … [2] (b) Find the nth term. … [2]

4 marks

Mark scheme: 18(a) 89, 111 2 B1 for each If 0 scored, SC1 for two terms with a difference of 22 18(b) 22 n − 21 oe final answer 2 B1 for final answers 22n + j or kn −21 k≠0 or for correct answer seen and spoilt

This question in 0580/12 Feb/March 2022

20 22, 17, 12, 7, 2, … (a) Find the next term of the sequence. … [1] (b) Find the nth term of the sequence. … [2]

3 marks

Mark scheme: 20(a) −3 1 20(b) 27 – 5n oe final answer 2 B1 for j – 5n or 27 – kn, k ≠0 or for 27 – 5n seen then spoilt

This question in 0580/11 May/June 2022

15 The nth term of a sequence is n 2 + 12 . (a) Find the first three terms of this sequence. … , … , … [2] (b) Is 5196 a term in this sequence? Give a reason for your decision. … because … … [2]

4 marks

Mark scheme: 15(a) 13, 16, 21 2 B1 for 2 correct terms in correct position or SC1 for 12, 13, 16 15(b) Yes 2 2 M1 for n  12  5196 or better n  72 or for a correct worded description for finding n or for 5184 is a square number

This question in 0580/12 May/June 2022

16 The nth term of a sequence is n 2 - 1. Find the first three terms of this sequence. … , … , … [2]

2 marks

Mark scheme: 16 0 3 8 2 B1 for 2 correct terms in correct position or SC1 for −1 0 3

This question in 0580/13 May/June 2022

17 (a) 3, 9, 27, 81, … Write down the term to term rule for this sequence. … [1] (b) 13, 17, 21, 25, … Find the nth term of this sequence. … [2]

3 marks

Mark scheme: 17(a) × 3 1 17(b) 4n + 9 oe final answer 2 B1 for 4n + k or jn + 9, j ≠ 0, or correct answer seen then spoilt

This question in 0580/11 Oct/Nov 2022

12 (a) These are the first five terms of a sequence. 27 26 23 18 11 Find the next two terms in the sequence. … , … [2] (b) These are the first five terms of a different sequence. 3 10 17 24 31 Find the nth term. … [2]

4 marks

Mark scheme: 12(a) 2 –9 2 B1 for one correct 12(b) 7n – 4 oe final answer 2 B1 for 7n + c or kn – 4 (k ≠ 0 ) as final answer or correct answer spoilt

This question in 0580/12 Oct/Nov 2022

17 (a) The nth term of a sequence is 10 - n 2 . Write down the first three terms of this sequence. … , … , … [2] (b) These are the first four terms of another sequence. 7 10 13 16 Find an expression for the nth term of this sequence. … [2]

4 marks

Mark scheme: 17(a) 9 6 1 2 B1 for 2 correct 17(b) 3n + 4 oe final answer 2 B1 for 3n + j or kn + 4 (k ≠ 0) or 3n + 4 seen and spoilt

This question in 0580/11 May/June 2023

3 These are the first four terms in a sequence. - 3 4 11 18 (a) Find the next term. … [1] (b) Explain how you worked out your answer. … [1]

2 marks

Mark scheme: 3(a) 25 1 3(b) Added 7 oe 1

This question in 0580/12 Oct/Nov 2023

20 (a) The nth term of a sequence is n 2 - 3 . Find the first three terms of this sequence. … , … , … [2] (b) These are the first five terms of a different sequence. 2 9 16 23 30 Find the nth term of this sequence. … [2]

4 marks

Mark scheme: 20(a) −2 1 6 2 B1 for any 2 in correct position If 0 scored SC1 for −−3, 2,1 20(b) 7n − 5 oe final answer 2 B1 for 7n + j or kn − 5, k  0 or 7n − 5 seen then spoilt

This question in 0580/12 Feb/March 2024

12 The table shows some information about two sequences. nth term 5th term Sequence A 60 – 4n Sequence B n2 – 300 Complete the table. [2]

2 marks

Mark scheme: 12 40 2 B1 for each –275

This question in 0580/11 May/June 2024

24 These are the first five terms of a sequence. 11 18 25 32 39 Find an expression for the nth term of the sequence. … [2]

2 marks

Mark scheme: 24 7n + 4 oe final answer 2 B1 for 7n + j or kn + 4 k ≠ 0 or 7n + 4 seen then spoilt

This question in 0580/11 May/June 2024

11 These are the first four terms of a sequence. 23 17 11 5 (a) Write down the next two terms. … , … [2] (b) Find the nth term. … [2]

4 marks

Mark scheme: 11(a) −1 −7 2 B1 for each If 0 scored, SC1 for two terms with a difference of −6 11(b) – 6n + 29 oe final answer 2 B1 for −6n + j or kn + 29 k ≠ 0 or – 6n + 29 oe seen but spoilt.

This question in 0580/12 May/June 2024

10 (a) These are the first four terms of a sequence. 3 10 17 24 (i) Write down the next term. … [1] (ii) Write down the term to term rule for continuing the sequence. … [1] (b) These are the first four terms of another sequence. 16 14 11 7 Write down the next two terms of this sequence. … , … [2]

4 marks

Mark scheme: 10(a)(i) 31 1 10(a)(ii) add 7 oe 1 10(b) 2 –4 2 B1 for each or 0 scored SC1 for two terms with a difference of −6

This question in 0580/13 May/June 2024

10 (a) These are the first four terms of a sequence. 10 16 22 28 Write down the next term in the sequence. … [1] (b) The term to term rule for another sequence is multiply by 3 and subtract 1. The fourth term in the sequence is 68. Find the third term in the sequence. … [2]

3 marks

Mark scheme: 10(a) 34 1 10(b) 23 nfww 2 M1 for 3[…] – 1 = 68 oe or better

This question in 0580/11 Oct/Nov 2024

6 These are the first four terms of a sequence. 19 26 33 40 (a) (i) Find the next term. … [1] (ii) Write down the term to term rule for this sequence. … [1] (b) These are the first four terms of another sequence. -1 2 5 8 Find the nth term of this sequence. … [2]

4 marks

Mark scheme: 6(a)(i) 47 1 6(a)(ii) Add 7 oe 1 6(b) 3n – 4 2 B1 for 3n + j or kn – 4 k ≠ 0, or 3n – 4 seen then spoilt

This question in 0580/13 Oct/Nov 2024

5 Find the next term in each sequence. (a) 1, 5, 10, 16, 23, … … [1] (b) 1, 2, 4, 8, 16, … … [1]

2 marks

Mark scheme: 5(a) 31 1 5(b) 32 1

This question in 0580/13 May/June 2025

7 These are the first four terms of a sequence. 9 5 1 -3 (a) Find the next term. … [1] (b) Explain how you worked out your answer. … [1]

2 marks

Mark scheme: 7(a) –7 1 7(b) Subtracted 4 oe 1

This question in 0580/11 Oct/Nov 2025

27 (a) These are the first four terms of a sequence. 2 8 14 20 Find the nth term of this sequence. … [2] (b) The nth term of a different sequence is n 2 + 10 . Find the first three terms of this sequence. … , … , … [2]

4 marks

Mark scheme: 27(a) 6n – 4 oe final answer 2 B1 for 6n + c or kn – 4 (k ≠ 0) or 6n – 4 seen and spoilt 27(b) 11 14 19 2 B1 for two correct terms in the correct places

This question in 0580/12 Oct/Nov 2025

21 These are the first four terms of a sequence. – 6 1 8 15 (a) Write down the next term. … [1] (b) Write down the term-to-term rule. … [1] (c) (i) Find the nth term. … [2] (ii) Is 688 a term in this sequence? Explain how you decide. … because … … [2]

6 marks

Mark scheme: 21(a) 22 1 21(b) Add 7 1 21(c)(i) 7n – 13 oe final answer 2 B1 for 7n + j or kn – 13 k ≠ 0, or 7n – 13 seen then spoilt 21(c)(ii) 7n – 13 = 688 oe 1 FT their nth term an + b 7n = 701 if a > 1 and b ≠ 0 No, 701 is not divisible by 7 oe nfww 1

This question in 0580/13 Oct/Nov 2025