Phillip received 75 points on a project for school. He can make changes and receive two-tenths of the missing points back. He can make corrections as many times as he wants.
Create the formula for the sum of this geometric series, and explain your steps in solving for the maximum grade Phillip can receive. Identify this as converging or diverging.
Answer (2)
The geometric sequence of the missing points is:
a is the missing points initially. Assuming 100 marks, this is 25
r = 8/10, as the missing marks reduces by 2/10 each time
u n = 25 ( 10 8 ) n − 1
Assuming the marks are out of 100, and marks are rounded to the nearest whole number, the maximum mark he can get is 98 , as 2/10 of the remaining 2 marks would make it 98.4, which would round back to 98.
This series is converging, as the 8/10 gets smaller every time, so the series will eventually converge.
Hope this helps :)
Phillip can recover the missing 25 points through a geometric series with a sum of recoverable points converging to 25, resulting in a maximum score of 100. The series is converging because the common ratio is less than 1. Thus, he is able to achieve a perfect score on his project.
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