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Algebra 1

4.14.3 The Connection between Sequences and Terms

Algebra 14.14.3 The Connection between Sequences and Terms
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Activity

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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.

A row of six circles: the first three circles are blue, a gap, then the last three circles are red. All circles are outlined in black and set against a green background.

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

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

Number of Checkers 1 2 3 4 7 8
Number of Moves Needed 3 8 15 24 63 ?

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

Try It: Using a Table to Find Missing Values

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

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