Pattern Building
| Site: | Clare-Gladwin RESD |
| Course: | Michigan Algebra II KHauck |
| Book: | Pattern Building |
| Printed by: | Guest user |
| Date: | Sunday, 19 May 2024, 9:56 PM |
Description
Pattern Building
A sequence is a set of numbers in a particular order.
Here is an example of a sequence:
1, 4, 7, 10, 13 …
Each of the numbers in the sequence is called a term of the sequence.
The key to any sequence is to find the pattern in the terms. A pattern that adds a constant from one term to the next is an arithmetic sequence and is modeled by a linear function. A pattern that multiplies a constant from one term to the next is a geometric sequence and is modeled by an exponential function. Other patterns create other sequences and can be modeled by many different families of functions.
Examples
Example 1 Find the pattern in the following sequence of numbers:
1, 4, 7, 10, 13, 16, 19 …
The sequence goes from one term to the next by adding 3 each time. Therefore, it is arithmetic and can be modeled by a linear function. The method for finding the function will be presented later in this unit.
Example 2 Find the pattern in the following sequence of numbers:
2, 6, 18, 54, 162 …
The sequence goes from one term to the next by multiplying by 3 each time. Therefore, the sequence is geometric and can be modeled by an exponential function. The method for finding the function will be presented later in this unit.
Example 3 Find the pattern in the following sequence of numbers:
-1, 4, 11, 20, 31, 44 …
In this sequence, there is no constant difference or ratio. To change from term 1 to term 2, add 5. To change from term 2 to term 3, add 7. To change from term 3 to term 4, add 9. This pattern will continue from term to term and has a common second difference.
Therefore, the sequence is not arithmetic or geometric and can be modeled by a quadratic function. The method for finding the function will be presented later in this unit.
Video Lesson
To learn how to find patterns in sequences, select the following link:
Extending Arithmetic SequencesGuided Practice
To solidify your understanding of finding patterns, visit the following link to Holt, Rinehart, and Winston Homework Help Online. It provides examples, video tutorials, and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.
Practice
*Note: If Google Docs displays, "Sorry, we were unable to retrieve the document for viewing," refresh your browser.
Answer Key
*Note: If Google Docs displays, "Sorry, we were unable to retrieve the document for viewing," refresh your browser.
Sources
Sources used in this book:
"Data Machine." http://www.tv411.org/mathgames/data.html (accessed 7/14/2010).
Embracing Mathematics, Assessment & Technology in High Schools; a Michigan Mathematics & Science Partnership Grant Project
Holt, Rinehart & Winston, "Extending Sequences." http://my.hrw.com/math06_07/nsmedia/lesson_videos/msm1/player.html?contentSrc=5993/5993.xml (accessed 7/14/2010).
Holt, Rinehart & Winston, "Whole Numbers and Patterns." http://my.hrw.com/math06_07/nsmedia/homework_help/msm1/msm1_ch01_07_homeworkhelp.html (accessed 7/14/2010).