Let 2x and 16x2(x>0) be the first and the last terms of a sequence in which three numbers are inserted so that the entire sequence forms a geometric progression.
a. (i) Calculate the three inserted numbers in terms of x.
b. (ii) Show that the product of the first and third inserted numbers is equal to the square of the second inserted number.
c. (iii) Hence, find the numerical values of the three inserted numbers when x=3.