Consider a geometric progression whose first term is a.
a. (i) Prove that if the common ratio is 1, then the sum of the first n terms is na.
b. (ii) When a=5 and the common ratio is 1, the sum of the first n terms is 40. Find n.
c. (iii) Keeping a=5, suppose the common ratio is changed to 1.2. Determine the least positive integer n for which the sum of the first n terms exceeds 40.