Question

A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles. How many miles did the hiker travel on the first day? Round your answer ti the nearest mile and show all necessary math work.

Answer 1

Given:

The increase in distance per day is 10%.

The sum of the nth term in the geometric progression is given as,

`S_n=(a(r^n-1))/(r-1),r>1`

The distance traveled after seven days is 75.897 miles.

`\begin{gathered} S_7=75.897 \\ r=1+(10)/(100)=(11)/(10) \\ S_7=\frac{a(((11)/(10))^7^{}-1)}{(11)/(10)-1} \\ 75.897=(a(0.9487171))/((1)/(10)) \\ 7.5897=a(0.9487171) \\ a=7.99 \\ a\approx8 \end{gathered}`

Answer: On the first day, the hiker travels 8 miles.