Skip to content
QuizQuip
Sign up
Back to Topic 8
Mark schemePDF

Topic 8 Practice Paper: Sequences — question paper

QuizQuipPractice Series
QQ/IGCSE-MATHS/T8

IGCSE · Cambridge IGCSE Mathematics (Extended (Core + Extended))

Topic 8 Practice Paper

Sequences

Duration: 40 minutes
Total: 30 marks
Name:
Class:
Register No.:
Date:

READ THESE INSTRUCTIONS FIRST

  • Answer all questions.
  • Section A contains ten multiple-choice questions. Choose one answer, A, B, C or D, for each.
  • Section B contains structured questions. Write your answers in the spaces provided.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total mark for this paper is 30.

Original practice material written against the Cambridge IGCSE Mathematics syllabus. It is not an official Cambridge examination paper. Topic 8: term-to-term rules, nth terms of linear, quadratic and cubic sequences, geometric (exponential) patterns, and term-hunting questions on patterns and positions.

For Examiner’s Use
Section A/ 10
Section B/ 20
Total/ 30

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

  1. 1

    What comes after 11, 15, 19, 23 in this list?

    1. A25
    2. B27
    3. C31
    4. D26
    ( )
  2. 2

    For 7, 12, 17, 22, …, the rule for term n is

    1. A5n − 2
    2. B5n + 7
    3. C5n + 2
    4. D7n − 5
    ( )
  3. 3

    Given the rule 4n − 3 for every term, work out term number 15.

    1. A57
    2. B60
    3. C63
    4. D45
    ( )
  4. 4

    Which expression generates 9, 4, −1, −6, …?

    1. A5n + 14
    2. B−5n + 4
    3. C−5n − 4
    4. D−5n + 14
    ( )
  5. 5

    Write down the next term of 1, 3, 9, 27, ….

    1. A72
    2. B81
    3. C90
    4. D243
    ( )
  6. 6

    Substituting n = 1, 2, 3, 4 into 2n² − 1 gives

    1. A2, 6, 12, 20
    2. B1, 4, 9, 16
    3. C1, 7, 17, 31
    4. D0, 5, 14, 27
    ( )
  7. 7

    Evaluate the term in position 6 of the sequence whose rule is 2ⁿ. (Extended)

    1. A64
    2. B32
    3. C128
    4. D12
    ( )
  8. 8

    108 sits in which position of the sequence generated by 7n − 4?

    1. A15th
    2. B108th
    3. C14th
    4. D16th
    ( )
  9. 9

    Which rule matches the list 3, 6, 11, 18, …?

    1. An² − 2
    2. Bn² + 2
    3. C2n²
    4. Dn² + 3
    ( )
  10. 10

    Tripling from a start of four generates 4, 12, 36, 108, … Its position-n formula is (Extended)

    1. A4 × 3ⁿ
    2. B12 × 3ⁿ
    3. C4 × 3ⁿ⁻¹
    4. D4 × 3ⁿ⁺¹
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show all your working.

  1. 11

    A sequence starts 96, 89, 82, 75, ….

    1. (a)

      Continue the list for two more terms.

      [1]
    2. (b)

      Find the nth term of the sequence.

      [2]
    3. (c)

      Is 0 one of the terms? Justify your answer.

      [2]
  2. 12

    A sequence has nth term n² + 3n.

    1. (a)

      Write down the first four terms.

      [2]
    2. (b)

      One of the terms is 130. Which position does it occupy?

      [3]
  3. 13

    A sequence starts 625, 125, 25, 5, …. (Extended)

    1. (a)

      Write down the two terms that follow the 5.

      [1]
    2. (b)

      Find an expression for the nth term.

      [3]
    3. (c)

      Which term equals 1⁄25?

      [1]
  4. 14

    Dots are arranged in triangles: pattern 1 has 1 dot, pattern 2 has 3 dots, pattern 3 has 6 dots, pattern 4 has 10 dots. (Extended)

    1. (a)

      Write down the number of dots in pattern 5.

      [1]
    2. (b)

      Show that the second differences are constant.

      [1]
    3. (c)

      Prove that the number of dots in pattern n equals n(n + 1)⁄2.

      [2]
    4. (d)

      Determine whether 120 dots can form one of these triangles.

      [1]

— End of paper —