Arithmetic Sequence

What's a sequence?

1,3,5,7,9

That's a sequence. Usually it is a set of numbers in order.

So what's an arithmetic sequence?

An arithmetic sequence is a bunch of numbers in order where the difference between each consecutive term is CONSTANT.

Quite a mouthful, but it actually isn't that hard.

Here's an example:

7, 10, 13, 16, 19, 22, 25...

As you can see all you need to do is to add 3 to get the next term. And this doesn't change! You just add 3, and add 3, and add 3...

As you can see, the difference between numbers next to each number doesn't change. Thus, they are constant. This is what makes a sequence an arithmetic sequence.

You can also express an arithmetic sequence in a formula, for example 5n-2. By subbing n with a value, you can find the nth term.

In an arithmetic sequence, the difference between the consecutive numbers is known as the common difference. The common difference can be negative or positive.

Try and find the common difference for these arithmetic sequences below:

1) 5, 10, 15, 20, 25, 30

2) 8, 9, 10, 11, 12, 13

3) 4, 6, 8, 10, 12

4) 100, 67, 34, 1

5) 0, 1, 3, 8, 9, 81

(Answers: 1) +5 2) +1 3) +2 4) -33 5) Not an arithmetic sequence!)

So how do we know the nth term of an aritmetic sequence?

Now, if you look closely, you'd see a pattern among the numbers.

Let's take a look at an arithmetic sequence: 2, 7, 12, 17, 22, 27

Common Difference

nth term : term