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Algebra 1

4.15.2 Using Tables and Graphs to Represent Geometric Sequences

Algebra 14.15.2 Using Tables and Graphs to Represent Geometric Sequences

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Activity

Clare takes a piece of paper, cuts it in half, and then stacks the pieces. She takes the stack of two pieces and cuts it in half again to form four pieces, stacking them. She keeps repeating the process.

1. The original piece of paper has length 8 inches and width 10 inches. Complete the table.

number of cuts number of pieces area in square inches of each piece
0    
1    
2    
3    
4    
5    

2. Describe in words how you can use the results after 5 cuts to find the results after 6 cuts.

3.

a. Use the graphing tool above or technology outside the course, on the given axes, sketch a graph of the number of pieces as a function of the number of cuts.

b. How can you see on the graph how the number of pieces is changing with each cut?

4.

a. Use the graphing tool above or technology outside the course, on the given axes, sketch a graph of the area of each piece as a function of the number of cuts.

b. How can you see how the area of each piece is changing with each cut?

Are you ready for more?

Extending Your Thinking

1. Clare has a piece of paper that is 8 inches by 10 inches.

a. How many pieces of paper will Clare have if she cuts the paper in half n n times?

1.

b. What will the area of each piece be?

2. Why is the product of the number of pieces and the area of each piece always the same? Explain how you know.

Self Check

Self Check

Given the table below, what would be the next term in the sequence?

x 1 2 3 4 5
y 270 90 30 10 10 3
  1. 10 27
  2. 10 9
  3. 11 3
  4. 10 6

Additional Resources

Graphs of Sequences

Graph the sequence {18, 36, 72, 144, 288, . . .}.

First, make a table:

Term 1 2 3 4 5
Value 18 36 72 144 288

Now, plot the points:

A scatter plot shows points increasing rapidly, with n values 1 to 6 on the x-axis and aₙ values 0 to 360 on the y-axis, indicating a nonlinear, accelerating growth pattern.

Notice that each height is double the previous height.

Each term is also double the previous term.

Try it

Try It: Graphs of Sequences

Graph the following sequence and explain the pattern.

1, 3, 9, 27, . . .

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