How do you find the nth term of a linear sequence?

There are two things to find, using an example sequence will help illustrate what we do:

3, 7, 11, 15

We are looking to write this as an+b

The first thing we need to find is the common difference between terms in the sequence. In this case, it is 4. We then put this number in front of n, so a=4. So our rule will contain 4n.

Now we look at what more we need to do. We do this by substituting n=1 and comparing with our first term.

So here, we have 4+b=3. So we find that b=-1.

And that's our rule: 4n-1