An infinite geometric progression has positive first term a and common ratio r. The sum to infinity of the series is 12, while the sum of its first three terms is 10.
a. (i) Write expressions for the sum to infinity and for the sum of the first three terms of the series in terms of a and r.
b. (ii) Using the given numerical values, form two equations in a and r.
c. (iii) Solve the equations to find the values of a and r, and comment on whether the obtained r satisfies the convergence condition.