Two arithmetic progressions are given as follows:
Progression R: first term 2 and common difference 5,
Progression S: first term 17 and common difference 2.
(i) Find the positive integer n for which the n-th terms of the two progressions are equal.
(ii) Determine that common term.
(iii) Calculate the sum of the first n terms of each progression.
(iv) Find the difference between these two sums.