# Thread: Rules for evaluating the general terms of seqences

1. ## Rules for evaluating the general terms of seqences

$\displaystyle a_n=n+(n+1)+(n+2)+.....+(2n)$

The question was to evaluate the first 4 terms. I came up with several ways I thought could be correct. For me it was I was not sure of the correct way of interpreting the math grammer. If I did exactly what it said I would wind up with infinity for every value of n. So I assumed that was not right and that it means to take the $\displaystyle \sum$ of n terms.

Are there any standard rules that help in deciphering this. Like rules of grammer for english or orders of operations in math. It seems that this "formula" in particular is ambiguous to me, so I assume I don't know the proper way of reading such. The way they switched the form of the terms realy threw me off. My nearest guess to a "rule" patern is as follows.

1) Individual terms will be grouped by parentheses. The n number will determine the amount of terms.
2) Sub in the number whereever you see it in the equation.
3) Always include the last term in the sumation if it differs from the form of the rest of the terms.

Are these correct statements of rules? If not could you advise me as to the correct rules, further if me rule list is not complete could you complete it?

I guessed three possibilities and one was right, But I would like to know the proper way of interpreting it. I am not interested in the answer to the above homework problem as I did get that resolved. I am interested in the principle behind it.

2. Originally Posted by manyarrows

$\displaystyle a_n=n+(n+1)+(n+2)+.....+(2n)$

The question was to evaluate the first 4 terms. I came up with several ways I thought could be correct. For me it was I was not sure of the correct way of interpreting the math grammer. If I did exactly what it said I would wind up with infinity for every value of n. So I assumed that was not right and that it means to take the $\displaystyle \sum$ of n terms.
Do as it says: Add up the terms, starting with $\displaystyle n$ and increasing by 1, until you get to $\displaystyle 2n.$ If it helps, note that $\displaystyle 2n=n+n,$ so you will be adding $\displaystyle n+1$ terms.

For example,

$\displaystyle a_3=3+(3+1)+(3+2)+(3+3)=3+4+5+6=18.$

We stop with 6 because $\displaystyle 6=2\cdot3=2n.$

1) Individual terms will be grouped by parentheses.
Only if the grouping is necessary to clearly separate each term in the summation.

The n number will determine the amount of terms.
No, not necessarily. In problems like the one given, yes, $\displaystyle n$ will affect the number of terms in each element of the sequence.

2) Sub in the number whereever you see it in the equation.
Well, that is the idea. This is how the definition is supposed to be interpreted.

3) Always include the last term in the sumation if it differs from the form of the rest of the terms.
I am not sure what you mean by this. When evaluating the term, you should use the full given form.