Skip to ContentGo to accessibility page
OpenStax Logo
Algebra 1

4.14.3 The Connection between Sequences and Terms

Algebra 14.14.3 The Connection between Sequences and Terms

4.14.3 The Connection between Sequences and Terms

4.14.3 • The Connection between Sequences and Terms

Activity

Access multimedia content

Some checkers are lined up, with blue on one side, red on the other, and 1 empty space between them. A move in this checker game pushes any checker forward 1 space, or jumps over any 1 checker of the other color. Jumping the same color is not allowed, moving backward is not allowed, and 2 checkers cannot occupy the same space.

You complete the puzzle by switching the colors completely: ending up with black on the right, red on the left, and 1 empty space between them.

1. Using 1 checker on each side, complete the puzzle. What is the smallest number of moves needed?

2. Using 3 checkers on each side, complete the puzzle. What is the smallest number of moves needed?

3. Estimate the number of moves needed if there are 2 or 4 checkers on each side. Then test your guesses.

4. Noah says he used the solution for 3 checkers on each side to help him solve the puzzle for 4 checkers. Describe how this might happen.

5. How many moves do you think it will take to complete a puzzle with 7 checkers on each side?

Self Check

The table below shows the number of checkers and the number of moves needed to win a skipping game.

Number of Checkers 1 2 3 4
Number of Skips Needed 2 8 18 32

How many skips are needed with 6 checkers on each side?

  1. 48
  2. 128
  3. 72
  4. 50

Additional Resources

Using a Table to Find Missing Values

What is the pattern that you used in the previous activity to find the number of moves depending on the number of checkers?

Each row is multiplied by 1 more, so:

1·3=31·3=3

2·4=82·4=8

3·5=153·5=15

4·6=244·6=24

How many moves are needed with 5 checkers?

5·7=355·7=35 moves

What about 6 checkers?

6·8=486·8=48 moves

Try it

Using a Table to Find Missing Values

Using the table and the pattern, how many moves are needed with 8 checkers?

PreviousNext
Order a print copy
Citation/Attribution
Reuse and redistribution of this content in digital or print format:
  • This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's prior written permission.
  • This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License, which means that you can reuse and modify the material only for noncommercial purposes, must attribute OpenStax, and must distribute any derivative works under the same license.
  • Any commercial printing of this textbook, including using a local or custom printer, must be approved by OpenStax, and proper citation provided.
  • OpenStax-copyrighted images, activities, assessments, and similar components of this book are subject to the same licensing – CC-BY-NC-SA. They can be used for noncommercial purposes with attribution. Commercial use requires permission.
  • Permission requests: Anyone who intends to incorporate this content (including text, images, and other components) into large language models, use it in AI offerings, use it commercially (including in print), and/or has questions about another use case is welcome to complete our reuse request form.
Attribution information
  • If you are redistributing all or part of this book in a noncommercial print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a noncommercial digital format, then for every page that includes OpenStax content, you must license the derivative work under the same CC-BY-NC-SA license as the original, and include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

The information below includes the information needed to generate citations in most major styles (APA, MLA, etc.); you must reformat and organize the information as needed to fit the requirements of the style. Use the information below to generate a citation. We recommend using a citation tool such as this one.

© Apr 23, 2026 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo, and Rice University name, and Rice University logo trademarks, or wordmarks are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.