A student decides to save money each month so that the amounts saved form an arithmetic progression.
a. (i) In the first month the student saves Rs 500, and in the twelfth month the student saves Rs 1045. Find the common difference of the progression.
b. (ii) Obtain a formula for Sn, the total amount saved in the first n months.
c. (iii) Using the result of part (ii), determine the total amount saved in the first 12 months.
d. (iv) After how many months will the student have saved at least Rs 50,000 in total? (Assume the same pattern continues.)