Consider the geometric progression 240, 120, 60, 30, \dots defined for positive integers n.
a. (i) Identify the common ratio r and write the general term an of the progression in terms of n.
b. (ii) By examining the value of r, explain whether the sequence of partial sums Sn approaches a finite limit as n becomes very large. Give a brief reason for your answer without explicitly using any summation formula.
c. (iii) Calculate S6, the sum of the first six terms, and comment on how its value supports the conclusion you reached in part (ii).