View by Category

Loading...

PPT – Arithmetic Sequences PowerPoint presentation | free to view - id: 1e76e1-MzEwN

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Arithmetic Sequences

- Math SPIRAL 2003
- University of Maryland
- Fredericka Blackwell, Spelman College
- Travis Bolden, Morehouse College
- Caiyan Chen, Trinity College
- Amina Pleasant-Bey, Trinity College

Outline of Presentation

- Describe the Arithmetic Sequence Game
- Provide strategies for finding an arithmetic

sequence in a specified game - Explain cases for which one player will win a

game - State the results of experiments
- Questions/Comments

The Game

- An arithmetic sequence is a sequence in which the

difference between any two consecutive terms is

the same. - i.e. 2, 4, 6 or -2,-5,-8
- Parameters n and k A game consists of the

counting numbers 1,2,3,,n, where k is the length

of the arithmetic sequence. (k lt n) - Players There are two players in this game,

Creator and Breaker. The Creator is the player

who is trying to make an arithmetic sequence of

length k. The Breaker is the player who is

trying to stop the creator from making the

arithmetic sequence.

Rules

- Step I Creator (Breaker) selects a number in

1,,n. - Step 2 Breaker (Creator) selects a number in

1,,n. - Step 3 If at the end of the game there is an

arithmetic sequence of length k, then the Creator

wins. Otherwise, the Breaker wins.

Demo I

- C Creator B Breaker
- k3 n5
- 1 2 3 4 5
- C
- B C
- B C C
- B C B C
- C B C B C
- Creator wins!!!

Demo II

- C Creator B Breaker
- k3 n5
- 1 2 3 4 5
- C
- B C
- B C C
- B C C B
- B C C C B
- Creator wins!!!

Strategy I k3

- Every case where n is greater than 5 can always

be reduced to the n5 case by selecting a block

of five numbers and playing accordingly. - Example
- 1 2 3 4 5 6 7 8 9 10
- or
- 1 2 3 4 5 6 7 8 9 10 11 12

Strategy II

- If the Creator can choose k-1 numbers such

that there are two unblocked arithmetic sequences

of length k containing those k-1 numbers, then

the Creator wins on his/her next move. - Lets take a look at the overhead projector!!

Strategy IIk4

- In order for the Creator to win, n must be

greater than or equal to 15. The Creator must

force all of the Breakers moves until a double

threat is created. - Lets take a look at the overhead projector!!

Wrap Around Game

- The Wrap Around Game is similar to the original

game, however, in the Wrap Around Game the

Creator can gain an arithmetic sequence by using

any order that is equally spaced. - Example
- n5 sequences can contain (5,1,2), (5,2,4),

(4,1,3) etc.

Wrap Around Demo

- C Creator B Breaker
- k3 n7
- 1 2 3 4 5

6 7 - C

- B C
- B C

C - B C

B C - C B C

B C - Creator wins the wrap around game with sequence

(5,7,2) which, unlike the original game, is not

in increasing order.

Cases

Conjectures Original Game

- the value of n required for the

Creator to win with an arithmetic sequence of

length k provided player d goes first (d is

either the Creator (c) or the Breaker (b)) . - 3( ), where k4
- 3( ), where k4

Results

- If the Creator is player II, then the value of n

for the Original case must be larger than the

value of n if the Creator is player I. - As k increases, the value of n required for the

Creator to win will increase significantly.

Acknowledgements

- Bill Gasarch, Ph.D.
- University of Maryland
- Computer Science Dept.
- Stacey Nicholls, TA
- University of Maryland
- Applied Mathematics Dept.
- Tasha Inniss, Ph.D.
- Trinity College
- Mathematics Dept.

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Arithmetic Sequences" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Umd University and other schools with their online training by sharing educational presentations for free