Nth Term Questions with Answers

Free maths practice · Skills Lab

Nth Term Questions with Answers

Here are 12 nth term questions with answers for linear sequences, split into 7 levels that go from increasing sequences to working out which term a number is, or whether it is in the sequence at all. For a fresh set of 10 questions at any level, open the same skill in our free Skills Lab, which also steps through the working one line at a time.

  • 7levels, easiest first
  • 12questions on this page, with answers
  • 10fresh questions every time in the Lab
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A worksheet shows the answer. The Skills Lab shows how to get there. Pick a level and the working appears one step at a time, each time you press the button, so your child can follow every move and then try ten questions of their own.

Skills Lab teach mode working through finding the nth term step by step
Teach: the working, one step at a timeThe gaps between the terms are worked out in front of you, then the times table lines up underneath the sequence.
Skills Lab practise mode with ten finding the nth term questions
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Practise finding the nth term in the Skills Lab

How to find the nth term of a linear sequence

Find the difference between the terms. That number goes in front of n. Write out its times table under the sequence, then work out what you add or take away to get from the times table to the sequence. That number finishes the nth term.

Find the nth term of 5, 8, 11, 14, …

  1. The difference is 3, so the nth term starts 3n
  2. 3n gives 3, 6, 9, 12
  3. Each term is 2 more, so the nth term is 3n + 2

Which term of 3n + 2 is 62? Is 100 a term?

  1. 3n + 2 = 62, so 3n = 60 and n = 20. 62 is the 20th term.
  2. 3n + 2 = 100, so 3n = 98 and n = 32.67
  3. n is not a whole number, so 100 is not a term

Nth Term Questions by level

Click a level to practise it
Level Question Question
Level 1Increasing sequences 1. 1, 8, 15, 22, … 2. −7, −4, −1, 2, …
Level 2Decreasing sequences 3. 23, 17, 11, 5, … 4. 14, 9, 4, −1, …
Level 3Picture patterns These questions are drawn as pictures, so try them in the Skills Lab.
Level 4Which term is it? 5. Which term of 8 − 7n is −314? 6. Which term of 1, −7, −15, −23, … is −247?
Level 5Is this number a term? 7. Is −126 a term of 24 − 9n? 8. Is −80 a term of 19 − 2n?
Level 6Decimal and fraction differences 9. 0.5, −0.1, −0.7, −1.3, … 10. 1/2, 0, −1/2, −1, …
Level 7Everything mixed 11. 4.5, 6.2, 7.9, 9.6, … 12. Is −56 a term of 9 − 8n?
Show all 12 answers
Question Answer
1. 1, 8, 15, 22, … 7n − 6
2. −7, −4, −1, 2, … 3n − 10
3. 23, 17, 11, 5, … −6n + 29
4. 14, 9, 4, −1, … −5n + 19
5. Which term of 8 − 7n is −314? 46
6. Which term of 1, −7, −15, −23, … is −247? 32
7. Is −126 a term of 24 − 9n? No
8. Is −80 a term of 19 − 2n? No
9. 0.5, −0.1, −0.7, −1.3, … −0.6n + 1.1
10. 1/2, 0, −1/2, −1, … −1/2n + 1
11. 4.5, 6.2, 7.9, 9.6, … 1.7n + 2.8
12. Is −56 a term of 9 − 8n? No

Common mistakes

  • Writing n + 3 instead of 3n. The difference multiplies n. A sequence that goes up in 3s has 3n in its nth term.
  • Missing the minus on a decreasing sequence. 20, 17, 14, … goes down by 3, so the nth term starts −3n. It is −3n + 23.
  • Checking only the first term. Test your answer with n = 1 and n = 2. If both work, the rule is right.

Questions parents and students ask

What is the nth term?

It is a rule that gives any term of a sequence from its position n. For 3n + 2, the 10th term is 3 × 10 + 2 = 32.

How do you know if a number is in a sequence?

Set the nth term equal to the number and solve for n. If n is a positive whole number, it is a term.

Is the nth term on the 11+?

Some 11+ papers ask for the rule of a sequence or the 10th or 20th term. The nth term itself is taught in Key Stage 3 and tested at GCSE.

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