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Year 8 · Key Stage 3 · free KS3 maths worksheet

Sequences

12 original questions, 36 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Write down the missing numbers in each sequence.

  1. 5   9   ___   17   ___
  2. 40   ___   28   22   ___
  3. 3   6   12   ___   48
3 marks
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a) 13 and 21 b) 34 and 16 c) 24
2

Here is a sequence.

4   11   18   25   ...

  1. Write down the 3rd term.
  2. Write down the term-to-term rule.
  3. Write down the position of the term 25 in the sequence.
  4. Is this an arithmetic sequence or a geometric sequence? Give a reason.
4 marks
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a) 18 b) add 7 c) 4th (position 4) d) Arithmetic: it goes up by the same amount (7) each time
3
  1. The first term of a sequence is 7. The term-to-term rule is "multiply by 2 then subtract 3". Write down the first four terms.
  2. The first term of another sequence is 50. The term-to-term rule is "subtract 8". Write down the first five terms.
3 marks
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a) 7, 11, 19, 35 b) 50, 42, 34, 26, 18
4

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
5

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
6

Here are the first four terms of an arithmetic sequence.

5   9   13   17

Find an expression, in terms of n, for the nth term of the sequence.

2 marks
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4n + 1
7

Here are the first four terms of an arithmetic sequence.

20   17   14   11

Find an expression, in terms of n, for the nth term of the sequence.

2 marks
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23 - 3n
8
  1. The nth term of a sequence is 4n + 3. Write down the first three terms and work out the 20th term.
  2. The nth term of another sequence is 30 − 2n. Write down the first three terms.
3 marks
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a) 7, 11, 15 and the 20th term is 83 b) 28, 26, 24
9

Here are the first three patterns in a sequence made from square tiles.

  1. Draw Pattern 4 in the space on the right.
  2. How many tiles are in Pattern 10?
  3. Find an expression, in terms of n, for the number of tiles in Pattern n.
Pattern 1Pattern 2Pattern 3Pattern 4
4 marks
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a) Pattern 4: a row of 5 tiles with a row of 4 tiles on top (9 tiles) b) 21 c) 2n + 1
10

Here are the first four terms of an arithmetic sequence.

7   12   17   22

Explain why 81 is not a term of this sequence.

2 marks
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Every term of the sequence ends in 2 or 7, and 81 ends in 1
11

The nth term of a sequence is 5n − 3

  1. Work out the 12th term of the sequence.
  2. Is 122 a term of the sequence? You must show how you get your answer.
3 marks
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a) 57 b) Yes, 5n - 3 = 122 gives n = 25, a whole number
12

The nth term of a sequence is 7n − 4.

  1. Show that 150 is a term of the sequence and write down its position.
  2. Is 200 a term of the sequence? Give a reason.
  3. Work out the first term of the sequence that is greater than 100.
4 marks
Show answer
a) 7n - 4 = 150 gives n = 22, a whole number, so it is the 22nd term b) No: 7n - 4 = 200 gives n = 29.14..., not a whole number c) 101

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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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