Sequences

Check out this list of numbers. π

32, 34, 36, 38, 40, 42, ...

Does it follow a pattern? π€

Yes! π Each number goes up by 2.

Lists like this are called **sequences!**

A **sequence **is a list of numbers that follows a **pattern or rule.**

π Some examples of sequences are:

0, 1, 2, 3, 4, 5, ...

5, 10, 15, 20, 25, 30, ...

A sequence has **3 parts:** terms, a rule, and an ending.

** Terms **are the numbers that form a sequence.

For example, the terms of the above sequence π are **0, 2, 4, 6, 8, etc.**

A **rule or pattern** is the specific order that a sequence follows.

For example, the **rule **for the above sequence π is **+2.**

A sequence can stop after a few terms, or go on forever.

If a sequence goes on forever, we put **3 dots (...) **at the end, called **ellipsis.**

The dots (...) in the above sequence π tell us that it goes on forever.

Here's an example of a sequence that **does not go on forever**:

4, 8, 12, 16, 20

Sequences can **count up **or** down.**

Sequences that count **up **are called **forward sequences.**

For example, this is a forward sequence:

Sequences that count **down **are called **backward sequences.**

For example, this is a backward sequence:

To find the **rule **of a sequence, just find out how to get from one term to the next.

π For example,

Let's try to **find the rule **of this sequence.

0, 6, 12, 18, 24, 30, ...

What happens to **0 (the first term) **to make it **6 (the second term)**?

That's right! π

0+ 6= 6

Similarly,

6+ 6= 12

So, the rule of this sequence is **+6.**

π Let's try another example.

Find the rule of this sequence.

84, 81, 78, 75, 72, ...

Where do we start?

πWe look at change between the first and second terms!

What happens to **84 **to turn it into **81?**

You got it! π€

84- 3= 81

So, the rule of the sequence is **-3.**

Great work! π

Check out this sequence.

15, 30, ____, ____, 75, 90

It's missing some terms!

How can we find them? π€

To **find **the **missing terms **in a sequence, first find the **rule. **Then **use it **to find the missing terms.

Let's try it!

What's the **rule **of the above sequence? π€

π To find out let's look at the first 2 terms.

15+ __= 30

To go from one term to the next, we add 15!

15+ 15= 30

So, the rule of the sequence is **+15. β
**

Now let's **use this rule** to find the missing terms.

What comes after 30 in the sequence?

30+ 15=45

45+ 15=60

That's it! π

The missing terms of the sequence are** 45 and 60.**

15, 30, 45, 60, 75, 90

Great job! π

Now you're ready to ace some practice questions.

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