In an arithmetic progression, the 4th term and the 8th term are in the ratio 5 : 9. The 6th term of the same progression is 41.
a. (i) Form two equations in the first term a and the common difference d using the given information.
b. (ii) Solve the equations to find a and d.
c. (iii) Determine the 20th term.
d. (iv) Find the sum of the first 25 terms of the progression.