Unit 1, Lesson 2
Introducing Geometric Sequences
Algebra 2
2.2
Activity
Clare takes a piece of paper, cuts it in half, then stacks the pieces. She takes the stack of two pieces, cuts it in half again to form four pieces, and then stacks them again. She keeps repeating the process.
- The original piece of paper has length 8 inches and width 10 inches. Complete the table.
number
of cutsnumber
of piecesarea, in square inches,
of each piece0 1 2 3 4 5 - Describe in words how you can use the results of the number of pieces and the area of each piece after 5 cuts to find the results after 6 cuts.
- On the given axes, sketch a graph of the number of pieces as a function of the number of cuts. How can you see on the graph how the number of pieces is changing with each cut?
- On the given axes, sketch a graph of the area of each piece as a function of the number of cuts. How can you see how the area of each piece is changing with each cut?