Given:
The increase in distance per day is 10%.
The sum of the nth term in the geometric progression is given as,
[tex]S_n=\frac{a(r^n-1)}{r-1},r>1[/tex]The distance traveled after seven days is 75.897 miles.
[tex]\begin{gathered} S_7=75.897 \\ r=1+\frac{10}{100}=\frac{11}{10} \\ S_7=\frac{a((\frac{11}{10})^7^{}-1)}{\frac{11}{10}-1} \\ 75.897=\frac{a(0.9487171)}{\frac{1}{10}} \\ 7.5897=a(0.9487171) \\ a=7.99 \\ a\approx8 \end{gathered}[/tex]Answer: On the first day, the hiker travels 8 miles.
