In this lesson, we are introduced to mathematical patterns. Our objectives are to identifu mathematical patterns and learn how to use a formula to find the nth term in a sequence.
There are several new vocabulary terms... -Sequence-ordered list of numbers -term-each number in the sequence and are labled with subscripts -Recursive Formula-defines t he terms in a sequence by relating each term to the ones before. In order to use this formula, you must know the preceding term in the sequence. -Explicit Formula-a formula that expresses the nth term in terms of n.
Example One: Describe the pattern and find the next two terms.
2,4,6,8... How to describe the patter-First you have to check and make sure that it is a regular repeating pattern. To do that, you take the second term [4] and the first term [2] and subtract them from each other. However, you have to subtract them opposite the normal way. In order to get the correct answer you have to subtract 4-2=2. So, your common difference [you will learn about this in lesson 2] is 2. So, to find the next two terms, you simply at two to the last term and you get 10. Then add two to 10 and you get 12, and then you could find any term in the sequence if you kept going in that pattern.
Example Two: Using the Recursive Formula: To use the recursive formula, all you do is find the pattern in your sequence and add it to the last term to get the term you need.
-2,-1,0,1,2...find the next two terms.
The pattern in this sequence is adding one. So, to get the next term-- 1+2=3. Then--3+1=4. So the next two terms are 3 and 4.
In summary-today's lesson was really all about learning mathematical patterns. We learned what a Recursive and Explicit formula is. Today's lesson was the basics for what you will learn later on in this chapter :)
I teach AP Calculus, Pre AP Precalculus, and Advanced Algebra/Trigonometry at Muscle Shoals High School. In my spare time, I enjoy spending time with my family and granddaughters. My husband and I like to travel and visited Germany and France last summer. I also enjoy reading, art and music.
Last spring, I read The Other Boleyn Girl by Philippa Gregory. I am currently reading the Constant Princess (by the same author).
I love "anything about England".
"SUGGESTED READING LIST" The Mathematical Traveler. It is a great book that combines history and interesting facts about famous mathematicians. See me if you want to "check it out".
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In this lesson, we are introduced to mathematical patterns. Our objectives are to identifu mathematical patterns and learn how to use a formula to find the nth term in a sequence.
There are several new vocabulary terms...
-Sequence-ordered list of numbers
-term-each number in the sequence and are labled with subscripts
-Recursive Formula-defines t he terms in a sequence by relating each term to the ones before. In order to use this formula, you must know the preceding term in the sequence.
-Explicit Formula-a formula that expresses the nth term in terms of n.
Example One:
Describe the pattern and find the next two terms.
2,4,6,8...
How to describe the patter-First you have to check and make sure that it is a regular repeating pattern. To do that, you take the second term [4] and the first term [2] and subtract them from each other. However, you have to subtract them opposite the normal way. In order to get the correct answer you have to subtract 4-2=2. So, your common difference [you will learn about this in lesson 2] is 2.
So, to find the next two terms, you simply at two to the last term and you get 10. Then add two to 10 and you get 12, and then you could find any term in the sequence if you kept going in that pattern.
Example Two:
Using the Recursive Formula:
To use the recursive formula, all you do is find the pattern in your sequence and add it to the last term to get the term you need.
-2,-1,0,1,2...find the next two terms.
The pattern in this sequence is adding one. So, to get the next term-- 1+2=3. Then--3+1=4. So the next two terms are 3 and 4.
In summary-today's lesson was really all about learning mathematical patterns. We learned what a Recursive and Explicit formula is. Today's lesson was the basics for what you will learn later on in this chapter :)
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