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Special sequences: AQA GCSE Maths questions

Every AQA GCSE Maths exam question on A24 Special sequences, 2017–2025, with its mark scheme and examiner’s report.

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1,304 questions

  1. Q4

    November 2024 · Paper 1H

    3 marksA24 Special sequences
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    November 2024 Paper 1H, question 4: (a) Write the missing term in the geometric progression. 1 4 16 256 4 (b) A Fibonacci-type sequence begins 5 –9 The sequence is continued by adding the previous

  2. Q23

    June 2024 · Paper 1H

    4 marksA24 Special sequencesN8 Exact calculation and surds
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    June 2024 Paper 1H, question 23: (a) The first three terms of a geometric progression are 5 2 5 4 5 5 8 Work out the next term. Answer 23 (b) The nth term of a sequence is (2 + 3 )n Show that t

  3. Q1

    June 2024 · Paper 3H

    2 marksA24 Special sequences
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    June 2024 Paper 3H, question 1: Here are the first three Patterns in a sequence made up of small squares. 1 (a) On the grid, draw Pattern 4 1 (b) The expression for the number of small squares

  4. Q25

    November 2023 · Paper 1H

    2 marksA24 Special sequences
    The whole paper ↗
    November 2023 Paper 1H, question 25: The nth term of a geometric progression is rn where r > 0 The second term is 9 8 Work out the third term. Give your answer in the form c d 2 where c and d are i

  5. Q9

    November 2023 · Paper 2H

    3 marksA6 Identities and algebraic proofA24 Special sequences
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    November 2023 Paper 2H, question 9: Here is the term-to-term rule for a sequence. The first three terms of the sequence are a + 1 2a + 5 4a + 13 Show that the sum of the first four terms is a mult

  6. Q2

    June 2023 · Paper 2H

    1 markA24 Special sequences
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    June 2023 Paper 2H, question 2: Four consecutive triangular numbers are 6 10 15 21 Write down the next triangular number. Answer

  7. Q9

    November 2022 · Paper 2H

    1 markA24 Special sequences
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    November 2022 Paper 2H, question 9: The 47th triangular number is 1128 The 48th triangular number is 1176 Work out the 49th triangular number. Answer

  8. Q7

    November 2022 · Paper 3H

    4 marksA24 Special sequencesA25 The nth term
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    November 2022 Paper 3H, question 7: (a) Here is the rule for a sequence. The 1st term is 33 The 2nd term is x The 4th term is 73 Work out the value of x. After the first two terms, each term is th

  9. Q19

    June 2022 · Paper 1H

    3 marksA24 Special sequences
    The whole paper ↗
    June 2022 Paper 1H, question 19: The first three terms of a sequence are x y xy The sequence is continued by multiplying the previous two terms. 19 (a) Circle the 5th term of the sequence. x3y3

  10. Q3

    June 2022 · Paper 2H

    1 markA24 Special sequences
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    June 2022 Paper 2H, question 3: Circle the triangular number. 9 12 15 18

  11. Q7

    June 2022 · Paper 3H

    4 marksA25 The nth termA24 Special sequences
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    June 2022 Paper 3H, question 7: A is an arithmetic progression. Here are the first four terms. 13 16 19 22 G is a geometric progression. Here are the first four terms. 2 4 8 16 Work out the va

  12. Q3

    November 2021 · Paper 2H

    1 markA24 Special sequences
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    November 2021 Paper 2H, question 3: The first three terms of a geometric progression are 3 2 9 4 27 8 Circle the fourth term. 81 10 81 14 81 16 81 32

  13. Q9

    November 2020 · Paper 1H

    5 marksA24 Special sequences
    The whole paper ↗
    November 2020 Paper 1H, question 9: (a) All the terms of a geometric progression are positive. The second and fourth terms are shown. ………. 4 ………. 16 Work out the first and third terms. First term

  14. Q6

    November 2019 · Paper 1H

    3 marksA24 Special sequences
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    November 2019 Paper 1H, question 6: (a) A geometric progression starts 4 16 Work out the next term. Answer 6 (b) A Fibonacci-type sequence starts 3 –8 The sequence is continued by adding the previ

  15. Q12

    June 2019 · Paper 1H

    1 markA24 Special sequences
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    June 2019 Paper 1H, question 12: The next term of a sequence is made by adding the previous two terms. Which of these sequences follows this rule? Circle your answer. –9 2 –7 –5 –12 –3 5 –2 3 1

  16. Q3

    November 2018 · Paper 2H

    1 markA24 Special sequences
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    November 2018 Paper 2H, question 3: Which of these is a geometric progression? Circle your answer. 1 3 5 7 9 1 3 6 10 15 1 4 9 16 25 1 3 9 27 81

  17. Q5

    June 2018 · Paper 2H

    4 marksA24 Special sequences
    The whole paper ↗
    June 2018 Paper 2H, question 5: Match each sequence to its description. One has been done for you.

  18. Q10

    November 2017 · Paper 2H

    2 marksA24 Special sequences
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    November 2017 Paper 2H, question 10: Work out the next term of this quadratic sequence. 5 8 14 23 …… Answer

  19. Q3

    June 2017 · Paper 1H

    1 markA24 Special sequences
    The whole paper ↗
    June 2017 Paper 1H, question 3: Which of these is a geometric progression? Circle your answer. 2, 4, 6, 8, 10 2, 3, 5, 8, 12 2, 6, 18, 54, 162 2, 6, 10, 14, 18

  20. Q9

    Specimen · Paper 1H

    3 marksA24 Special sequences
    The whole paper ↗
    Specimen Paper 1H, question 9: The nth term of a sequence is 2n + 1 The nth term of a different sequence is 3n  1 Work out the three numbers that are in both sequences and between 20 and 40
All 22 questions on Special sequences, as a list
  1. November 2024, Paper 1H, Q4 (3 marks): (a) Write the missing term in the geometric progression. 1 4 16 256 4 (b) A Fibonacci-type sequence begins 5 –9 The sequence is continued by adding the previous
  2. June 2024, Paper 1H, Q23 (4 marks): (a) The first three terms of a geometric progression are 5 2 5 4 5 5 8 Work out the next term. Answer 23 (b) The nth term of a sequence is (2 + 3 )n Show that t
  3. June 2024, Paper 3H, Q1 (2 marks): Here are the first three Patterns in a sequence made up of small squares. 1 (a) On the grid, draw Pattern 4 1 (b) The expression for the number of small squares
  4. November 2023, Paper 1H, Q25 (2 marks): The nth term of a geometric progression is rn where r > 0 The second term is 9 8 Work out the third term. Give your answer in the form c d 2 where c and d are i
  5. November 2023, Paper 2H, Q9 (3 marks): Here is the term-to-term rule for a sequence. The first three terms of the sequence are a + 1 2a + 5 4a + 13 Show that the sum of the first four terms is a mult
  6. June 2023, Paper 2H, Q2 (1 mark): Four consecutive triangular numbers are 6 10 15 21 Write down the next triangular number. Answer
  7. November 2022, Paper 2H, Q9 (1 mark): The 47th triangular number is 1128 The 48th triangular number is 1176 Work out the 49th triangular number. Answer
  8. November 2022, Paper 3H, Q7 (4 marks): (a) Here is the rule for a sequence. The 1st term is 33 The 2nd term is x The 4th term is 73 Work out the value of x. After the first two terms, each term is th
  9. June 2022, Paper 1H, Q19 (3 marks): The first three terms of a sequence are x y xy The sequence is continued by multiplying the previous two terms. 19 (a) Circle the 5th term of the sequence. x3y3
  10. June 2022, Paper 2H, Q3 (1 mark): Circle the triangular number. 9 12 15 18
  11. June 2022, Paper 3H, Q7 (4 marks): A is an arithmetic progression. Here are the first four terms. 13 16 19 22 G is a geometric progression. Here are the first four terms. 2 4 8 16 Work out the va
  12. November 2021, Paper 2H, Q3 (1 mark): The first three terms of a geometric progression are 3 2 9 4 27 8 Circle the fourth term. 81 10 81 14 81 16 81 32
  13. November 2020, Paper 1H, Q9 (5 marks): (a) All the terms of a geometric progression are positive. The second and fourth terms are shown. ………. 4 ………. 16 Work out the first and third terms. First term
  14. November 2019, Paper 1H, Q6 (3 marks): (a) A geometric progression starts 4 16 Work out the next term. Answer 6 (b) A Fibonacci-type sequence starts 3 –8 The sequence is continued by adding the previ
  15. June 2019, Paper 1H, Q12 (1 mark): The next term of a sequence is made by adding the previous two terms. Which of these sequences follows this rule? Circle your answer. –9 2 –7 –5 –12 –3 5 –2 3 1
  16. November 2018, Paper 2H, Q3 (1 mark): Which of these is a geometric progression? Circle your answer. 1 3 5 7 9 1 3 6 10 15 1 4 9 16 25 1 3 9 27 81
  17. June 2018, Paper 2H, Q5 (4 marks): Match each sequence to its description. One has been done for you.
  18. November 2017, Paper 2H, Q10 (2 marks): Work out the next term of this quadratic sequence. 5 8 14 23 …… Answer
  19. June 2017, Paper 1H, Q3 (1 mark): Which of these is a geometric progression? Circle your answer. 2, 4, 6, 8, 10 2, 3, 5, 8, 12 2, 6, 18, 54, 162 2, 6, 10, 14, 18
  20. Specimen, Paper 1H, Q9 (3 marks): The nth term of a sequence is 2n + 1 The nth term of a different sequence is 3n  1 Work out the three numbers that are in both sequences and between 20 and 40
  21. Specimen, Paper 2H, Q1 (1 mark): Which sequence is a geometric progression? Circle your answer. 1 2 3 4 1 2 4 7 1 2 4 8 1 2 3 5
  22. Specimen, Paper 3H, Q14 (2 marks): (a) The nth term of a sequence is 2n + 2n – 1 Work out the 10th term of the sequence. Answer 14 (b) The nth term of a different sequence is 4(2n + 2n – 1) Circl

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