The numbers 7, 13, 19, 25, 31, … are written on a board.
(i) Define an arithmetic progression (AP).
(ii) Explain, with the help of successive differences, whether the sequence 7, 13, 19, 25, 31, … is an AP.
(iii) If an additional 9th term were written, would the difference between the 8th and 9th terms remain the same as that between the first two terms? Give reason for your answer without calculating the actual terms.