SequencesFEBRUARY 2015

VocabularyA sequence is an on-going list of numbers that are in a pattern.

Each number in the sequence is known as a term.

Understanding the Language of MathIn sequences we use “sub numbers” to talk about the individual terms.

means or 9 does not mean we are multiplying anything by 3 or doing anything to the third power.

150, 300, 450, 600, 750…

The first term in this example is 150. We call this .

The second term in this example is 300. We call this .

Types of Sequences

There are two main types of sequences: Arithmetic and Geometric.

We will talk about these more tomorrow.

Types of Sequences

For now, when finding a pattern look for what is being added, subtracted, multiplied or divided each time to find the next term.

For example, find the next 3 terms of the sequences.

-34, -64, -94, -124, …-154, -184, -214 (sub 30 each time)3, -15, 75, -375, …1875, -9375, 46875 (mult by -5 each time)

For example, find the next 3 terms of the sequences.

-1, 3, 7, 11, …15, 19, 23 (add 4 each time)400, 200, 100, 50, …25, 12.5, 6.25 (Divide by 2 each time)

Finding a sequence from a formula

To make this even more confusing, there are two types of formulas for sequences.

Explicit Formula

This formula helps us find any term we need to find.

It is very nice to have, sometimes difficult to create.

Example:

We can use this formula to find any term we want in the sequence. If I want the first term, I will plug a 1 into the equation where ever there is an n.

Example:

Work:

Our first term is 3.

Example:

Work:

Our second term is .

Example:

Work:

Our third term is .

Example:

Work:

Our fourth term is .

Example:

So the first 4 terms were: 3, , , If we needed to find more terms, we would plug more numbers in to n.

Recursive Formulas

This is another way to write a formula.

It is a simpler formula, however it isn’t as useful as the explicit formula.

First a review of MathJoey is a student in my class. I might refer to his age as x, because I am a crazy math teacher, or I just don’t know it.

If someone told me that Mary was a year older, I might think that her age is Joey’s age plus 1, or x+1.

First a review of MathIf someone told me that Sam was a year younger than Joey, I might say his age is x-1

Student Age

Sam x-1

Joey x

Mary x+1

Why I just told you that…

In a sequence, is the term that comes right before .

In a sequence, is the term that comes right before

2, 7, 12, 17, 22, …If you looked at this formula, you might just

say that you start on “2” and add five again and again and again.

That is what the recursive formula tells you to do.