Algebra II Geometric Series

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Sam recorded the height of each bounce of the ball, beginning with the height from which the ball originally fell, in the chart below:

 Ball 1 DescriptionBall 2 DescriptionBall 3 Description
Height 1
(starting point)
3 ft
3 ft
3 ft
Height 2
2.4
1.9
0.9
Height 3
1.9
1.2
0.3
Height 4
1.5
0.8
0.1
Height 5
1.2
0.5
0.02


Using complete sentences, answer the following questions:

  1. What is the average common ratio between the successive height values of ball 1? Ball 2? Ball 3? Experimental errors may cause common ratios to have some variances within the data for one ball. Use the average common ratio.
  2. What is the height of each ball on the fifth bounce (i.e., Height 6)? Use the geometric sequence formula, an = a1rn – 1 and show your work.
  3. What is the total distance of the height each ball has traveled in the first five heights? Use the geometric series formula, Sn = the quantity of a sub 1 minus a sub 1 times r to the n power, all over 1 minus r  and show your work.
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