Answer the following questions about inserting arithmetic means between two numbers.
(i) Define an arithmetic mean between two numbers.
(ii) Two distinct real numbers a and b are written in that order. Prove that if m arithmetic means are inserted between them so that all the resulting numbers form an arithmetic progression, then the common difference of the progression equals m+1b−a.
(iii) Using part (ii), obtain a general expression for the kth arithmetic mean between a and b (where 1≤k≤m).