Let the mth term of an arithmetic progression equal its nth term where m=n.
(i) Prove that the common difference of the progression must be zero.
(ii) What does this imply about every term of the progression? State your conclusion clearly.
(iii) If such a progression is represented on a Cartesian plane with term number on the x-axis and term value on the y-axis, describe the shape of the graph and justify your answer.