Here we will learn about how to find the nth term of a sequence. You’ll learn what the nth term is and how to work it out from number sequences and patterns.
At the end you’ll find nth term worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
The nth term refers to the position of a term in a sequence. For example the first term has n=1, the second term has n=2, the 10th term has n=10 and so on. The ‘n’ stands for its number in the sequence.
We can make a sequence using the nth term by substituting different values for the term number( n ).
To find the 20th term we would follow the formula for the sequence but substitute 20 instead of ‘ n ‘; to find the 50th term we would substitute 50 instead of n .
For example if the n th term = 2n + 1
1st term = 2(1) + 1 = 3
2nd term = 2(2) + 1 = 5
3rd term = 2(3) + 1 = 7
10th term = 2(10) + 1 = 21
Below are a few examples of different types of sequences and their n th term formula.
| Type of Sequence | Example | n th Term |
|---|---|---|
| Arithmetic | 6, 2, -2, -6, -10, . | 10-4n |
| Geometric | 1, 2, 4, 8, 16, 32, . | 2^ |
| Quadratic | 3, 9, 19, 33, 51, . | 2n^+1 |
| Cubic | 2, 22, 78, 188, 370, . | 3n^-n |
In this lesson, we will look specifically at finding the n th term for an arithmetic or linear sequence.