Number Patterns

12 Grade 6 Mathematics questions on Number Patterns, with worked marking schemes. 12 questions are available on this topic in full.

1. Question 1

   1 mark

   What is the rule for: 3, 7, 11, 15, 19?

   A. Add 3

   B. Add 5

   C. Add 4

   D. Multiply by 2

   (1 mark)

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2. Question 2

   1 mark

   A pattern starts at 500 and decreases by 45 each step. What is the 4th term?

   A. 320

   B. 410

   C. 365

   D. 355

   (1 mark)

   Marking scheme

   C. $365$ — the fourth term is three steps past the first: $500-3\times 45=365$. B is the third term, which is the usual off-by-one.

3. Question 3

   1 mark

   Find the missing number: 5, 10, 20, ___, 80

   A. 50

   B. 60

   C. 40

   D. 30

   (1 mark)

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4. Question 4

   1 mark

   What is the next number: 2, 6, 18, 54, ___?

   A. 72

   B. 162

   C. 108

   D. 216

   (1 mark)

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5. Question 5

   1 mark

   What is the 5th square number?

   A. 36

   B. 16

   C. 20

   D. 25

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6. Question 6

   1 mark

   Fill in: 1, 4, 9, 16, ___, 36

   A. 20

   B. 25

   C. 28

   D. 24

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7. Question 7

   1 mark

   Find the missing: 1, 1, 2, 3, 5, 8, ___

   A. 11

   B. 13

   C. 16

   D. 14

   (1 mark)

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8. Question 8

   1 mark

   What is the next term: 1, 3, 6, 10, 15, ___?

   A. 18

   B. 21

   C. 22

   D. 20

   (1 mark)

   Marking scheme

   B. $21$ — these are the triangular numbers, and the gaps grow by one each time: $2,3,4,5$, so the next gap is $6$ and $15+6=21$.

9. Question 9

   1 mark

   Find the missing: 100, 91, 82, 73, ___

   A. 64

   B. 63

   C. 62

   D. 65

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10. Question 10

    1 mark

    What is the 6th term in: 4, 9, 14, 19, 24, ___?

    A. 34

    B. 30

    C. 29

    D. 28

    (1 mark)

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11. Question 11

    1 mark

    What is the 10th term if the first term is 3 and common difference is 5?

    A. 50

    B. 53

    C. 48

    D. 45

    (1 mark)

    Marking scheme

    C. $48$ — the $10$th term is $9$ steps past the first, not $10$: $3+9\times 5=48$. B uses $10$ steps, which is the commonest slip here.

12. Question 12

    1 mark

    The pattern is: 2, 5, 10, 17, 26, ___. What comes next?

    A. 38

    B. 37

    C. 36

    D. 35

    (1 mark)

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