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| Site: | Clare-Gladwin RESD |
| Course: | Michigan Algebra II KHauck |
| Book: | Other |
| Printed by: | Guest user |
| Date: | Saturday, 18 May 2024, 9:15 PM |
Description
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Other
Many sequences do not follow the pattern of geometric or arithmetic. These sequences have their own patterns. Some can be modeled by other polynomial functions.Example 1 The following sequence models triangular numbers:
The symbolic pattern for this sequence is to add 2 to the first term, add 3 to the second term, add 4 to the fourth term and so on. This type of sequence has a constant second difference and can be modeled by the quadratic function 
.
Examples
Example 2 The following sequence models square numbers:Similar to the triangular numbers, square numbers make perfect squares from rows of dots. The symbolic pattern for this sequence can be modeled by the quadratic function
. Example 3 The following sequence models cube numbers.
The symbolic pattern for this sequence is to add 7 to the first term, add 19 to the second term, add 37 to the fourth term, and so on. This type of sequence has a constant third difference and can be modeled by the cubic function 
.
Guided Practice
To solidify your understanding of other sequences, 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.Guided Practice
Practice
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Answer Key
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Sources
Sources used in this book:Embracing Mathematics, Assessment & Technology in High Schools; a Michigan Mathematics & Science Partnership Grant Project
Holt, Rinehart & Winston, "Guided Practice." http://go.hrw.com/math/midma/gradecontent/loadlesson.html?course=c3&chapter=12&lesson=3&SE=1&sz_audio=1&calc=1&state=xx&actCourse=4 (accessed 7/14/2010).
Holt, Rinehart & Winston, "Sequences and Functions." http://my.hrw.com/math06_07/nsmedia/homework_help/msm3/msm3_ch13_03_homeworkhelp.html (accessed 7/14/2010).