## What you need to know

Things to remember:

• Linear sequences go up or down by the same amount each time.
• We are adding if the numbers are getting bigger going to the right.
• We are subtracting if the numbers are getting smaller going to the right.

So, what is a sequence? It is just the order that things come in, it doesn’t just have to be numbers.

The first two sequences you will have learned when you were younger are the alphabet and the 1 times table.

a          b          c          d          e          f

1          2          3          4          5          6

So, why do we use sequences, what’s the point? Sequences can help us see patterns, how things are increasing or decreasing, and predict what will happen next?

What comes after f in the alphabet?

G

What comes after 6 in the 1 times table?

7

There are lots of different types of sequences, like quadratic (ewww), exponential (double ewww), and linear. Luckily for you, we will just look at linear. You will see the other ones in about 4 years time……….

So, what is a linear sequence? It is just a sequence of numbers that goes up or down by the same amount each time?

Is the 1 times table a linear sequence?

1          2          3          4          5          6

Yes – it goes up by 1 each time.

Is the 7 times table a linear sequence?

7          14        21        28        35

Yes – it is going up by the same amount each time.

In fact, all of our times tables are linear sequences, because they’re going up by the same amount each time!

So, now to the real point of this topic, how do we describe a linear sequence? Simples, we just have to say how much it is going up or down by each time!

Describe the following linear sequence

8          11        14        17        20

So, to describe this sequence, we need to see how much it changes by each time. To do this, we choose two numbers that are next to each other and subtract the first one from the second one.

$$17-14=3$$

$$11-8=3$$

This sequence is going up by 3 each time.

Let’s try this for a sequence where the numbers are getting smaller.

Describe the following linear sequence

34        27        20        13        6

$$20-27=-7$$

$$6-13=-7$$

This sequence changes by -7 each time, so is going down by 7 each time.

## Example Questions

#### Question 1: Describe the following linear sequence:5          13        21        29        37

$$21-13=8$$

$$37-29=8$$

The sequence is going up by 8 each time.

#### Question 2: Describe the following linear sequence:33        28        23        18        13

$$28-33=-5$$

$$13-18=-5$$

This sequence changes by -5 each time, so is going down by 5 each time.