SOLUTION: A car travels 64 miles for the first hour, 32 miles for the second hour, and 16 miles for the third hour. If the car could decelerate at this rate forever, approximately how many m
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Question 1153971: A car travels 64 miles for the first hour, 32 miles for the second hour, and 16 miles for the third hour. If the car could decelerate at this rate forever, approximately how many miles would it travel total? Answer by ramkikk66(644) (Show Source):
This is an infinite geometric progression where the series starts with 64 and reduces to 50% every hour. 64,32,16,8,4...
The first term = 64
The ratio of the progression = 0.5
What is asked for is the total distance travelled which is the sum of this infinite series.
The sum of an infinite geometric series with first term as a1 and ratio as r is given by
Substituting for a1 and r, we get
Total distance =
Approximate total distance travelled =
(