Find the nth Term
11+ Maths, topic 7.5.1
Finding the 'nth Term'
When you are asked to find the ‘nth term’, you are being asked to find a rule that can be used to find the value of any step in a particular sequence.
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How to find the nth term
- You need to find a rule that takes you from the step number to the corresponding number in the sequence.
- So you need to find a rule that takes 1 to 5, 2 to 7, 3 to 9 and so on.
Work out the sequence difference
- First, work out the difference between the numbers in the sequence. This tells you how much you need to multiply 'n' by.
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Multiply by 2
- The difference between the numbers in the sequence is 2.
- So the first part of the rule is 'multiply by 2'.
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Add 3
- Next, work out what you need to add or subtract to get the number in the sequence.
- To get from 2 to 5, add 3. So the second part of the rule is 'add 3'.
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2n+3
- In algebra, we write the rule 'multiply by 2 and add 3' as 2n + 3 (we do not use the multiplication sign). This is the ‘nth term’.
Test yourself on Find the nth Term
What's the second part of the nth term for this sequence?
3, 11, 19, 27...
8n - ?What's the second part of the nth term for this sequence?
17, 15, 13, 11
-2n + ?What's the second part of the nth term for this sequence?
-11, -9, -7, -5
2n - ?What's the nth term of this sequence?
4, 9, 14, 19...What's the nth term of this sequence?
-1, 5, 11, 17...