Answer the following questions about the sum of the first n terms of an arithmetic progression (AP).
(i) State two different algebraic expressions that are commonly used to represent the sum of the first n terms of an AP. Clearly identify every symbol you use.
(ii) Without performing any numerical calculations, explain which of the two expressions is more convenient to apply when the last term of the AP is known but the common difference is not, and give a reason for your choice.
(iii) Give one specific example of an AP by writing its first four terms, for which the second expression you mentioned in part (i) would save time compared with the first. Justify your choice in two or three sentences.