An athlete follows a 40-day training plan. On the first day he runs 2 km. Each following day he increases the distance run by the same fixed amount. By the end of the 40th day he wants the total distance covered to be exactly 400 km.
(i) Find the daily increase in distance.
(ii) On which day will he first run at least 15 km in a single day?
(iii) If he continues the same pattern beyond the 40 days, determine the least day on which his cumulative distance will exceed 1,000 km.