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The nth term of a sequence: Year 9 maths

This topic covers finding and using the nth term rule for linear and simple quadratic sequences. The worksheet practises expressing sequences algebraically and calculating specific distant terms.

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What this covers

The nth term of a sequence is taught in Year 9 (age 13 to 14, KS3) as a topic to introduce. It sits in the Algebra strand.

Worked example

Find the nth term of the sequence: 5, 8, 11, 14, ...

  1. Find the common difference between terms: 8 - 5 = 3, so the rule contains 3n
  2. Compare 3n (3, 6, 9, 12) with the sequence: 5 - 3 = 2
  3. Combine the terms to get the nth term formula: 3n + 2

Answer: 3n + 2

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Finding the nth term of positive increasing linear sequences, e.g., 3, 7, 11, 15
  2. Finding the nth term of decreasing linear sequences, e.g., 20, 16, 12, 8
  3. Generating terms of a sequence given an algebraic nth term, e.g., find the 50th term
  4. Determining if a specific number belongs to a given sequence using equations
  5. Finding the nth term of simple quadratic sequences, e.g., n^2 + b or 2n^2 + 1

Common mistakes

  • Writing the difference as an addition rather than the coefficient of n, e.g. n + 4 instead of 4n
  • Confusing the term position n with the value of the term itself

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Deduce expressions to calculate the nth term of linear arithmetic sequences.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

The nth term of a sequence

Year 9 maths

Qs
6
Marks
12
NameDateScore / 12
1.
Find the nth term of 6, 14, 22, 30, ...
[2]
2.
Find the nth term of 11, 14, 17, 20, ...
[2]
3.
Find the nth term of 16, 24, 32, 40, ...
[2]
4.
Find the nth term of 9, 16, 23, 30, ...
[2]
5.
Find the nth term of 0, 3, 6, 9, ...
[2]
6.
Find the nth term of 6, 15, 24, 33, ...
[2]

Answer key

  1. 8n − 2The sequence goes up by 8, so the term starts 8n; 6 − 8 = -2, so the nth term is 8n − 2
  2. 3n + 8The sequence goes up by 3, so the term starts 3n; 11 − 3 = 8, so the nth term is 3n + 8
  3. 8n + 8The sequence goes up by 8, so the term starts 8n; 16 − 8 = 8, so the nth term is 8n + 8
  4. 7n + 2The sequence goes up by 7, so the term starts 7n; 9 − 7 = 2, so the nth term is 7n + 2
  5. 3n − 3The sequence goes up by 3, so the term starts 3n; 0 − 3 = -3, so the nth term is 3n − 3
  6. 9n − 3The sequence goes up by 9, so the term starts 9n; 6 − 9 = -3, so the nth term is 9n − 3