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Year 9 · 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

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
Show answer
a) 48 b) multiply by 2 (accept double the previous term)
2

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
Show answer
a) 2 and -1 b) subtract 3 (accept take away 3)
3

Here are four sequences.

A   4     9     14     19
B   1     4     9     16
C   2     6     18     54
D   1     1     2     3     5

For each sequence, write down

  1. the type of sequence: arithmetic, geometric, square numbers or Fibonacci-type
  2. the next term.
4 marks
Show answer
a) A arithmetic, B square numbers, C geometric, D Fibonacci-type b) A 24, B 25, C 162, D 8
4

The nth term of a sequence is 6n − 1

Write down the first three terms of the sequence.

2 marks
Show answer
5, 11, 17
5
  1. The nth term of a sequence is  20 − 3n
    Write down the first three terms and work out the 10th term.
  2. The nth term of another sequence is  n2 + 2
    Write down the first three terms.
3 marks
Show answer
a) 17, 14, 11; 10th term -10 b) 3, 6, 11
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
Show answer
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
Show answer
23 - 3n
8

Kwame makes patterns from square tiles.

Pattern 1 uses 6 tiles. Pattern 2 uses 10 tiles. Pattern 3 uses 14 tiles.

The number of tiles goes up by the same amount each time.

  1. Find an expression, in terms of n, for the number of tiles in Pattern n.
  2. Work out the number of tiles in Pattern 20
  3. Kwame says, "One of my patterns uses exactly 100 tiles." Is Kwame right? Show how you decide.
4 marks
Show answer
a) 4n + 2 b) 82 c) No - 4n + 2 = 100 gives n = 24.5, which is not a whole number
9

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
Show answer
a) 57 b) Yes, 5n - 3 = 122 gives n = 25, a whole number
10

Here are the first four terms of an arithmetic sequence.

8   15   22   29

  1. Find an expression, in terms of n, for the nth term of the sequence.
  2. Explain why 150 is not a term of the sequence.
4 marks
Show answer
a) 7n + 1 b) 7n + 1 = 150 gives 7n = 149, and 149 is not divisible by 7
11

Here are the first five terms of a quadratic sequence.

2   7   14   23   34

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

2 marks
Show answer
n2 + 2n - 1

Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.

12

Here are the first five terms of a quadratic sequence.

4     11     22     37     56

  1. Find an expression, in terms of n, for the nth term of the sequence.
  2. Work out the 10th term of the sequence.
5 marks
Show answer
a) 2n2 + n + 1 b) 211

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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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