In the previous section we looked at patterns represented by dots on a grid. In this section we will use matchsticks to represent patterns. We will also look at how some sequences can be described using simple algebra.
Look at the pattern below. We want to find the number of matches in the 10th shape.
The number of matches in each shape has been written underneath.
If we look at the number of matches we have added to each shape to get the next, we see that this is the same as the
differences in the sequence. The differences are:
We can now see that the differences are increasing by 2 each time. To find the next term after 54, we will add on 16.
The 7th term is 54 + 16 = 70
The 8th term is 70 + 18 = 88
The 9th term is 88 + 20 = 108
The 10th term is 108 + 22 = 130
We can now see that the 10th shape will have 130 matches in it.
We can use it to find the value of any term in the sequence, as long as we know its position. In the example above, we found the general rule that the nth term is always 4×n or 4n. If we want to know the 36th term we just put 36 in the rule instead of n: the 36th term is 4×36 = 144. 
