An arithmetic or linear sequence is one like this:

We see that the **common difference is 2.**

So, we can say the rule starts with** 2n**

The problem is that the first number we would get by doing 2n is 2 x 1 which gives us 2 when **we need to get 3!**

Therefore, its simple - **we just add 1**

**Answer = 2n + 1**

The best thing about this is that it means we can find **any t**erm in that sequence.

We know the rule is** 2n + 1**

To find the **150th term** simply substitute** n for 150** (n is the term number)

Like this!

**2 x 150 + 1 = 301**

If we want the **3,000th term** we can substitute **n for 3,000**

Like this!

**2 x 3,000 + 1 = 6,001**

How cool is that?

It also means we can generate the sequence from a rule given to us. How smart are we?

Let's take the rule 3n - 1 (generate the first five terms)

1st term will be when n = 1 3 x 1 - 1 = 2 (first term)

2nd term will be when n = 2 3 x 2 - 1 = 5 (second term) .......

We can save time here by cutting down the work!

We know the first term is 2 and the rule is **add 3 **so we can just add 3 to find the next ones.

**2, (2 + 3 = 5), (5 + 3 = 8), (8 + 3 = 11) etc .......**

**2, 5, 8, 11, 14, ........**

Let's do some questions to check you have got this!