Devin began running a month ago to get back in shape. the first day he ran. 5 miles. each day after that he ran 10% more than the previous day for a total of 30 days. use the formula for the sum of a finite geometric series to calculate the total distance devin ran over the 30 days.

Question

Madalyn Potter

Mathematics

1 May, 19:32

Devin began running a month ago to get back in shape. the first day he ran. 5 miles. each day after that he ran 10% more than the previous day for a total of 30 days. use the formula for the sum of a finite geometric series to calculate the total distance devin ran over the 30 days.

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Lauren Preston · Answer 1

The formula for the sum of the a finite geometric series is this:

Sn = a ((1-r^n) / (1-r))

The given values are:

n = 30

a = 0.5 mi

r = 1.10 (10% more each day)

S30 = 0.5 ((1-1.10^30) / (1-1.10))

S30 = 82.25 mi

After 30 days, he will have traveled 82.25 miles.