sum of arithmetic sequence

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??

Re: sum of arithmetic sequence

is the th term because is the first term, the second, ..., is the th term, hence is the th term.

Re: sum of arithmetic sequence

Quote:

Originally Posted by

**muddywaters** Given the arithmetic sequence

, and the sum of its first

terms is

, find

.

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??

In the sequence there are terms.

The first term is .

The second term is .

The last term is .