I'm sorry if this is in the wrong subforum, I am not sure where to put it. But I searched this topic and saw others posting in pre-calc so im posting this here.

Given the arithmetic sequence , and the sum of its first terms is , find .

the answer is this:

My question is this:

the part is from , where is the number of terms, is the first term and is the last term.

In this case, for the sum of terms, the last term is the term. the answer uses , which is the term, since it's directly after the term. it's not the term.

why is it like that? did i misunderstand something??