A student noted the number of push-ups completed each day for the first four days as 12, 17, 22 and 27.
(i) Determine whether the numbers recorded form an arithmetic progression. State the common difference, if any.
(ii) If the pattern continues, find the number of push-ups the student will complete on the 10th day.
(iii) After how many days from the start will the student first reach exactly 102 push-ups in a day? Show your working clearly.