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 2n

(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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