Odd sequences

Hi guys,

So I am not a mathematician but reaaally need to solve this sequence difference for my linguistics/ semantics class.
If I have a sequence such as {21, 22, 25, 26, 29, 30, 33, 34, 37, ...} in which the difference is always 1, 3, 1, 3, ... how could I describe this? I've been reading about the nth term and quadratic nth terms but nothing seems to fit due to the odd sequence!
I would really appreciate some help on this!

Jess

Simplest way to do this is to break it up into odd and even terms. Each of these is described by a simple linear equation.

I'm sorry I don't follow. I was thinking I can say it's a positive integer ≥ 25 but after that I just get stuck! I haven't learnt any math since I was 15/16 so this is proving as a bit of a challenge to say the least haha.

OK, let's call the nth term of the sequence $a_{n}$, then observe that if n is odd we can write

$\displaystyle a_{n} = 21 + \frac{n-1}{2} \times 4$

and if n is even we can write

$\displaystyle a_{n} = 22 + \frac{n-2}{2} \times 4$

Thanks for your help! Now a stupid question but what actually is n? Or do we have to work that out..?