An arithmetic progression is such that the ratio of the sum of its first 25 terms to the sum of its first 15 terms is 7 : 3. The 10th term of the progression is 29.
Answer the following questions based on this information.
a. (i) Frame an equation in the first term a and common difference d using the given ratio of the two sums.
b. (ii) Form a second equation in a and d using the information about the 10th term, and hence determine the values of a and d.
c. (iii) Using the values of a and d obtained in part (ii), find the 40th term of the progression.