First part of question:
Find the general term that represents the situation in terms of k.
The general term for geometric series is:

 = the first term of the series
 = the first term of the series
 = the geometric ratio
 = the geometric ratio
 would represent the height at which the ball is first dropped. Therefore:
 would represent the height at which the ball is first dropped. Therefore:

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:
 
Our general term would be: 


Second part of question:
If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.
 represents the initial height:
 represents the initial height:
 
 represents the number of times the ball bounces:
 represents the number of times the ball bounces:

Plugging this back into our general term of the geometric series:




 represents the highest height of the ball after 6 bounces.
 represents the highest height of the ball after 6 bounces.
Third part of question:
If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 
This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

We already know these variables: 
 
 

Therefore:



