Consider an arithmetic progression (AP) whose first term is a and common difference is d.
(i) State the general expression for the nth term of an AP in terms of a, d and n.
(ii) Explain, with reference to successive terms, why this expression correctly generates every term of the progression.
(iii) If the 1st, 2nd and 3rd terms of an AP are 7, 12 and 17 respectively, verify that they satisfy the expression stated in part (i).