AlgebraFoundation and Higher

Sequences: GCSE maths practice with worked answers

Show Working has 2 kinds of sequences question for GCSE Maths, for Foundation and Higher. Every question is new each time and comes with the working, step by step.

Sequence questions ask you to use an nth term rule to find a term, or to work out the nth term of a linear sequence from its first few terms. The difference between the terms tells you the number in front of n.

Coming soon to the App Store

Worked example 1: find a term from the nth term

The nth term of a sequence is −6n − 6. Work out the 10th term.

Replace n with 10: −6 × 10 − 6.
−6 × 10 = −60, then −60 − 6 = −66.

Answer -66

01 / What's covered2 kinds of question

Sequences questions in the app

Each kind makes fresh questions every time, so you can practise as often as you like.

Find a term from the nth termBoth tiers
Find the nth termBoth tiers

Worked example 2: find the nth term

Here are the first four terms of a sequence: 6, 3, 0, −3, ...
Find an expression for the nth term.

The terms go down by 3 each time. That is the common difference, so the nth term starts with −3n.
The sequence −3n goes −3, −6, −9, −12.
Compare it with 6, 3, 0, −3: each term is 9 more, so add 9.
So the nth term is −3n + 9.

Answer −3n + 9

A common mistake

Getting the sign of the difference wrong when the sequence goes down. For 6, 3, 0, −3 the difference is −3, so the nth term starts with −3n.

02 / Practise itiPhone and iPad

Practise sequences in Show Working

In the app, open Topics and choose Sequences for ten fresh questions. Ask for a hint if you are stuck, and open the working to see the method one step at a time.