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Grade 1 · Foundation · free GCSE maths worksheet

Continuing number sequences

Spotting the rule and finding the next terms.

13 original questions, 28 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Here are the first four terms of a sequence.

3    6    12    24

  1. Write down the next term of the sequence.
  2. Write down the term-to-term rule of the sequence.
2 marks
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a) 48 b) multiply by 2 (accept double the previous term)
2

Here is a sequence of numbers.

6, 11, 16, ____, 26

Work out the missing number.

1 mark
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21
3

Here are the first four terms of a sequence.

0.5, 1, 1.5, 2

Write down the next two terms.

2 marks
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2.5, 3
4

Here are the first five square numbers.

1    4    9    16    25

  1. Write down the next square number after 25.
  2. Write down the 8th square number.
2 marks
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a) 36 b) 64
5

Here are the first four terms of a sequence.

50, 44, 38, 32

  1. Write down the next two terms.
  2. Write down the rule for continuing the sequence.
2 marks
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a) 26, 20 b) subtract 6 each time
6

Matchsticks are used to make a row of squares. The table shows the number of matchsticks in the first three patterns.

Pattern number123
Number of matchsticks4710

The pattern carries on in the same way.

  1. Work out the number of matchsticks in Pattern 4.
  2. Work out the number of matchsticks in Pattern 6.
2 marks
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a) 13 b) 19
7

Here are the first five terms of a Fibonacci sequence.

2    3    5    8    13

  1. Write down the next term of the sequence.
  2. Describe the rule for finding the next term of the sequence.
2 marks
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a) 21 b) open: add the two previous terms together
8

Here are the first five terms of a sequence.

3, 8, 13, 18, 23

Eli says, "The number 100 will be in this sequence."

Is Eli correct? Give a reason for your answer.

2 marks
Show answer
No. Every term ends in 3 or 8, so 100 cannot be in the sequence (the terms near 100 are 98 and 103).
9

Here are the first four cube numbers.

1    8    27    64

  1. Write down the next cube number after 64.
  2. Write down the 10th cube number.
  3. Explain why 200 is not a cube number.
3 marks
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a) 125 b) 1000 c) open: 5 cubed = 125 and 6 cubed = 216, and 200 lies between them
10

Here are the first four terms of a sequence.

14    11    8    5

  1. Work out the next two terms of the sequence.
  2. Write down the term-to-term rule of the sequence.
3 marks
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a) 2 and -1 b) subtract 3 (accept take away 3)
11

Here are the first four terms of a sequence.

96    48    24    12

  1. Write down the next term of the sequence.
  2. Work out the 8th term of the sequence.
3 marks
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a) 6 b) 0.75 (accept 3/4)
12

Here are the first five triangular numbers.

1    3    6    10    15

  1. Describe how the sequence continues from one term to the next.
  2. Work out the next two terms of the sequence.
3 marks
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a) open: the amount added increases by 1 each time (add 2, add 3, add 4, ...) b) 21 and 28
13

The even numbers form the pattern

2,  4,  6,  8,  ...

Write down the 12th number in this pattern.

1 mark
Show answer
24

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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