1. ## Sequence

What is the formula for the nth term of the sequence “-1, 1, 3, 5,,…...”
for n = 1,2,…..

2. Uh, arithmetic progression? +2?

If you want to annoy your instructor, you can ask him/her what exactly they mean by "the formula for the nth term". The thing is that there is a (relatively) simple formula for any initial segment of a numerical sequence. I.e., given any finite sequence of numbers $\displaystyle y_1$, $\displaystyle y_2$, ... $\displaystyle y_n$, there is a function $\displaystyle f$ constructed from the four arithmetic operations such that $\displaystyle f(1)=y_1$, ..., $\displaystyle f(n)=x_n$. See Lagrange polynomial in Wikipedia.

But to do this, you need to feel that the course is boring enough so that you would like to go beyond and learn something that is indeed interesting. Otherwise, your instructor will parry your lunge and score after a counter-riposte...

3. Hello erinneedshelp
Originally Posted by erinneedshelp
What is the formula for the nth term of the sequence “-1, 1, 3, 5,,…...”
for n = 1,2,…..
This is an Arithmetic Progression with first term $\displaystyle a=-1$, common difference $\displaystyle d=2$. So the $\displaystyle n^{th}$ term is $\displaystyle a_n=a+(n-1)d=-1 +(n-1)2 = -3 + 2n$.