Welcome to Math III Please find a seat in a student desk where you will learn.

1. Your name 2. The name of your Math II teacher (and school if not at ADHS) 3. Your Math II grade 4. When you took Math II 5. What do you expect to learn this year. If you should not be in this course, where should you be. If you have an IEP, LEP, or 504, please indicate this.

About this course: Introduction Letter Course and pre-requisites Teacher Grades Bathroom Procedures Integrity MGS/Tutorial Electronics/Drinks Policy Supplies Notebook, paper, pencil, TI-84+ Donations of soft tissues and dry erase markers would be greatly appreciated

Website:

Warm-ups! Each day we will complete a warm-up. This is the warm- up structure: Draw this out on your own paper or print it from the website each week.

M3U1D1 Introduction to Math 3 Objective: To review notation and to define explicit and recursive forms. Explain Notebook Checks to students.

Arithmetic Sequences Geometric Sequences Arithmetic Series Geometric Series

a 4 indicates position. The 4 does not have a mathematical value. a 4 indicates a multiplied by itself four times.

Terminology/Notation Term – a number in a sequence a 1 -- represents the first term in a sequence (1 is the counter) a n -- the nth term in a sequence or the formula a n-1 -- the term before the nth term

Sequence Formulas For the sequence formula, a n = n solve the first 5 terms. 6, 9, 14, 21, 30

Consider the series 4, 8, 12, 16, 20, 24, … The third term in the series, a 3, is 12. What is the first term? What is the sixth term? What is the seventh term? a 1 = 4 a 6 = 24 a 7 = 28

In the previous example, we came up with the seventh term by looking at the pattern and applying it to the next term in the sequence. But what if we are asked to find the 150 th term? Today, we are going to look at 2 ways to write a rule (an equation) for finding the n th term in a series: explicit formula and recursive formula.

Explicit Formula With an explicit formula, we do not need to know what the previous terms are in order to calculate the next term. Let’s practice: Find the 150 th term: a n = n 2 – 4 22,496

Recursive Formula What does recursive mean? The dictionary defines recursive as pertaining to or using a rule or procedure that can be applied repeatedly. So, to simplify things, when you see recursive, I want you to think repeat.

Example of a recursive formula a 1 = 4 a n = a n Notice that the formula has 2 parts: 1. It defines the first term. In the above example, a 1 = It defines the remaining terms. In our example, a n =a n What does a n-1 mean???

Find the first six terms of the recursive sequence a 1 = 3 a n = a n a 1 = 3 a 2 = = 8 a 3 = = 13 a 4 = = 18 a 5 = = 23 a 6 = = 28 Repeat Repeat

If you wanted to find the 50 th term, you would have to repeat your calculations 50 times. Can you see why we associate recursive with repeat?

Just to summarize An explicit formula has only one equation. You can easily find any term in the sequence. ***** A recursive formula has 2 parts: the first term, and a rule, or equation, for finding the remaining terms based on knowing the previous term. In order to find the 50 th term, you will first have to find the previous 49 terms.

Homework: U1D1 HW WS AND have your parent read the class letter then sign & return the actual CCM III acknowledgement sheet to me.