(a(i))[2]
A marathon runner covers the opening mile in $5$ minutes. After that, each mile takes $12$ seconds more than the one before it. If the $n$th mile lasts $9$ minutes, calculate the value of $n$.
(a(ii))[2]
Suppose the marathon is $26$ miles long, calculate the total time, in hours and minutes, needed to finish the marathon.
(b)[4]
The second and third terms of a geometric progression are $48$ and $32$ respectively. Find the sum to infinity of the progression.