An athlete runs the first mile of a marathon in 5 minutes. His speed reduces in such a way that each mile takes 12 seconds longer than the preceding mile.
Given that the \(n\)th mile takes 9 minutes, find the value of \(n\).
Assuming that the length of the marathon is 26 miles, find the total time, in hours and minutes, to complete the marathon.
The second and third terms of a geometric progression are 48 and 32 respectively. Find the sum to infinity of the progression.