(Based on a general arithmetic progression)
An arithmetic progression (AP) has first term a and common difference d. Answer the following:
a. (i) Prove that the sum Sn of its first n terms can be expressed entirely in terms of a, d and n.
b. (ii) For the AP with a=7 and d=−3, determine the least positive integer n for which the sum of the first n terms is negative.
c. (iii) Using the value of n obtained in part (ii), calculate that negative sum.
d. (iv) Find the sum of the first 20 terms of the AP in part (ii).