Question

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.

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.