# Sequences

This lesson can be used for revision for the higher Maths GCSE. The examples are quick and concise with exam style questions, go to GCSE Maths if you need more in-depth explanations.

How to answer sequence questions in the GCSE exam?

There are 5 things that you are normally asked:
1) Find the next few
2) State the term to term rule
3) Find the nth term
4) Use the nth term
5) Determine if a number is in the sequence

Example 1: Here are the first five terms of a number sequence.
3, 8, 13, 18, 23
(a) Write down the next two terms of the sequence.
(b) Explain how you found your answer.
(c) Explain why 287 is not a term of the sequence.

Example 2: Here are the first five terms of a number sequence.
3, 7, 11, 15, 19
(a) Write down and expression, in terms of n, for the nth term of this sequence.
Adeel says that 319 is a term in the number sequence.
(b) Is Adeel correct? You must justify your answer.

Example 3: Here are the first five terms of an arithmetic sequence.
-1, 3, 7, 11, 15
(a) Find, in terms of n, an expression for the nth term of this sequence.
In another arithmetic sequence the nth term is 8n - 16
John says that there is a number that is in both sequences.
(b) Explain why John is wrong

Example 4: The nth term of a sequence is 2n2
(i) Find the 4th term of the sequence.
(ii) Is the number 400 a term of the sequence?
Give reasons for your answer.

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