In a league tournament, Team P scores 12 points in its first match and increases its score by 3 points in every subsequent match. Team Q scores 6 points in its first match and increases its score by 5 points in every subsequent match. Points scored per match by each team therefore form two arithmetic progressions.
Using this information, answer the following.
(i) Let Sn(P) and Sn(Q) denote the total points scored by Teams P and Q respectively after n matches. Write expressions for Sn(P) and Sn(Q).
(ii) Determine the least number of matches after which Team Q’s total points will be strictly greater than Team P’s total points.
(iii) For the number of matches obtained in part (ii), calculate the exact difference Sn(Q)−Sn(P).