What is the best way to prove this conjecture?

Okay, first post in the forums for me(Nod)

This is my first year in high school geometry (i'm a freshman) and I'm loving it! I've run into a spot of trouble though...

My geometry teacher challenged us with a problem, and if I get it right, he will give me an A for the semester. I don't have the exact conjecture written down, but basically it is a formula to find the nth term in a sequence. For example, this formula could tell you what the 65th term in the sequence 4, 7, 13, 21.... (1st difference is 3, 6, 9, 2nd difference is 3,3,3). I have yet to learn proofs, which is why this is a challenge.

From the research I have done, I figure that mathematical induction would be the best method. I am guessing that if I can prove it works for a difference of 1, I can prove it for 2,3,4,5, etc. Am I correct in my thinking? Is there a better method? Also, any advice in the process; this is my first time proving a theorem (and he said it IS a theorem, as he has already proven it). Thanks in advance!

I'll edit this tomorrow when I write down the formula, sorry about its absence right now. If any more information is needed, just ask. I look forward to helping out in the algebra section, and spending some time on these forums!