# The nth Term

## how to find the nth term of a sequence

Finding the nth term of a sequence is a popular GCSE topic which usually appears on the non calculator paper of your maths exam. After reading through the example question below check out the worksheets and practice questions.

## Example Question

Here is a sequence of numbers:

### 4, 10, 16, 22, 28

a) Write down the next two terms of the sequence.
b) Write down an expression for the nth term of this sequence.
c) Work out the 50th term of the sequence.

## Solution

a) From looking at the sequence we can see that each term is 6 larger than the previous term. We say the term-to-term rule is "add 6". Therefore the next two terms are 34 and 40.

b) The nth term of a sequence is always written in the form "?n + ?".

The number in front of the "n" is always the difference to get from one term to the next. Since the difference is 6, the first part of our rule will be "6n". The rule follows the six times table: 6, 12, 18, 24... etc.

Now compare the 6 times table with our rule:

 6 x table 6 12 18 24 30 Sequence 4 10 16 22 28

The numbers in the sequence are always 2 less than the 6 times table so we "adjust" our rule by subtracting 2. Now putting this together gives us:

### nth term = 6n - 2.

c) Now we know the nth term = 6n - 2 we just need to substitute n = 50 in order to find the 50th term of the sequence.

So: The 50th term = 6 x 50 - 2
= 300 - 2
= 298

## Test Yourself!

Here is a sequence of numbers:

### 14, 19, 24, 29, 34

a) Write down the next term of the sequence.
b) Write down an expression for the nth term of this sequence.
c) Work out the 40th term of the sequence.

### Practice GCSE questions:

Or try this step by step guide guide to finding the nth term of a sequence.