Question

You are responsible to provide tennis balls for a tournament. You know that a ball bounces like new when it is dropped and it bounces 82% of the previous height. Because of budget restriction for the tournament you need to test some used balls to make sure they bounce like new tennis balls. You drop a ball and it bounces multiple times; each bounce reaches 82% the height of the previous height. a. Is this sequence geometric or arithmetic? Explain. b. What are the heights of the first four bounces of a new ball if it is dropped from a height of 10 feet? c. What is an equation that will find the th term of this sequence? d. Does this sequence diverge or converge? Explain. e. What is the sum of the heights of the bounces for the first ten bounces of a new ball if it is dropped from 10 feet?

Answer 1

Answer:

Explanation:

a) It is a geometric sequence and 0.82 is the common ratio.

b) h = first term initial height of that the ball was released from

h₁ = 10 × 0.82 = 8.2

h₂ = 8.2 × 0.82 = 6.724

h₃ = 6.724 × 0.82 = 5.513

h₄ = 5.51368 × 0.82 = 4.52

c) since it is a geometric sequence

the general formula can be denoted by

Un = h ( r ) ^ n-1 = h ( 0.82) ^n-1

d) This sequence is converging since r is less than 1 ( 0.82 < 1),

e) sum of a geometric progression = h ( 1 - r^n) / ( 1 - r) since r is less than 1

sum of gp = 10 ( 1 - 0.82¹⁰) / ( 1 - r) = 8.62552 / 0.18 = 47.92