Find the nth tern of the sequence
-3,5,-7,9
$\displaystyle T_{n} = (-1)^n (2n + 1)$
First ignore the negatives.
It's easy to see that the n-th term is then given by $\displaystyle T_{n} = (2n + 1)$
Now we see that every odd term ($\displaystyle T_1$ , $\displaystyle T_3$ , etc.) is negative.
So all we do is multiply the expression by $\displaystyle (-1)^n$ where $\displaystyle n$ is the term. So if it's and odd term, it will have a negative value and a positive value for an even term.