IM Alg2.1.2 Lesson: Introducing Geometric Sequences

What do you notice? What do you wonder?
[list][*]40, 120, 360, 1080, 3240[/*][*]2, 8, 32, 128, 512[/*][*]1000, 500, 250, 125, 62.5[/*][*]256, 192, 144, 108, 81[/*][/list]
Clare takes a piece of paper, cuts it in half, then stacks the pieces. She takes the stack of two pieces, then cuts in half again to form four pieces, stacking them. She keeps repeating the process.
The original piece of paper has length 8 inches and width 10 inches. Complete the table.
Describe in words how you can use the results after 5 cuts to find the results after 6 cuts.[br][br]
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 number of pieces as a function of the number of cuts.
How can you see how the area of each piece is changing with each cut?
Clare has a piece of paper that is 8 inches by 10 inches.
How many pieces of paper will Clare have if she cuts the paper in half [math]n[/math] times?
What will the area of each piece be?
Why is the product of the number of pieces and the area of each piece always the same? Explain how you know.
Complete each geometric sequence. For each sequence, find its growth factor.
Fechar
– GeoGebra Classroom Activities, IM Algebra 1, Geometry, Algebra 2

Informação: IM Alg2.1.2 Lesson: Introducing Geometric Sequences