Answer the following questions with respect to an arithmetic progression (A.P.).
(i) Define an arithmetic progression and state what is meant by its common difference.
(ii) Explain, with the help of a general term pair, how adding the first and the last terms, the second and the second-last terms, and so on, leads to a constant sum for each pair when the first n terms of an A.P. are written in reverse order beneath the original list.
(iii) Using the idea explained in part (ii), write the formula for the sum Sn of the first n terms of an A.P. in terms of its first term a and common difference d.
(iv) Comment on whether the formula obtained in part (iii) changes if the common difference is negative, giving a brief reason for your answer.