In an arithmetic progression the p-th term is q and the q-th term is p, where p and q are distinct positive integers.
a. (i) Show that the (p+q)-th term of the progression is 0.
b. (ii) Hence obtain expressions for the first term and the common difference in terms of p and q.
c. (iii) Using the result of part (ii), determine the first term and the common difference when p=4 and q=7.