In an arithmetic progression, the nth term exceeds the first term by 30. The sum of the first n terms is 180. All terms are integers and the common difference is a positive integer.
a. (i) Form two equations in n, a and d based on the information given.
b. (ii) Show that (n−1)d=30 and list all possible integer pairs (n,d).
c. (iii) For each pair obtained in (ii), find the corresponding first term of the progression.