Foundation & Higher

Sequences: GCSE Maths revision

A sequence is a list of numbers with a rule. Linear (arithmetic) sequences go up or down by the same amount. The nth term lets you find any term without listing them all.

Linear nth term

If the common difference is d, the nth term is dn + c. Find c using the first term.

3, 7, 11, 15, …

Difference = 4 → 4n
When n = 1, 4(1) = 4 but the first term is 3, so subtract 1.
nth term = 4n − 1

Try these questions

Cover the answers and have a go first. Worked solutions are underneath.

Question 1 [1 mark]

Find the next two terms of 5, 8, 11, 14, …

Question 2 [2 marks]

Find the nth term of 2, 6, 10, 14, …

Question 3 [2 marks]

Is 50 in the sequence 4n + 1?

Question 4 [1 mark]

Find the 20th term of 3n + 2

Question 5 [1 mark]

The nth term is n². Write the first four terms.

Common mistakes

Answers and working

Q1. 17, 20
Q2. 4n − 2
Q3. No. 4n + 1 = 50 → n = 12.25, not a whole number.
Q4. 62
Q5. 1, 4, 9, 16

Frequently asked questions

What is a common difference?

The amount you add (or subtract) each time in an arithmetic sequence.

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