Topics · Edexcel GCSE Maths (1MA1)

The nth term of a linear sequence

Foundation and Higher

The nth term is a rule that gives any term from its position. Find the rule for this sequence.

Exam-style questionNon-calculator2 marks

Here are the first four terms of an arithmetic sequence.

5, 9, 13, 17

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

See why

Which rule gives the sequence 5, 9, 13, 17, 21?

Rule: $n$

n	1	2	3	4	5
Your rule	1	2	3	4	5
Sequence	5	9	13	17	21

Number of n (a)1Number added (b)0

Your terms go up by 1. The sequence goes up by 4.

New contextNon-calculator2 marks

The $n$ th term of a sequence is $3n - 7$

Which term of the sequence is equal to 53?

The nth term of a linear sequence

Short hands-on steps, then exam questions on this topic.

Specification A25: deduce expressions for the nth term of linear sequences (Higher adds quadratic sequences).
On both tiers.
Follow-up parts ask whether a number is in the sequence: set the rule equal to it and check for a whole-number position.