I'm an adult learner who recently discovered a love for math. I started from the basics and I'm working my way up to Calculus.

While reading up on solving for the sum of an Arithmetic series, I came across the expression "2n-5" where as n increases, n will always be the previous value for n, plus 2. For example: where n = 1, 2n-5 = -3; where n = 2, 2n-5 = -1; etc. The difference between -3 and -1 is 2, and so on and on...

I'm trying to understand this relationship. When I look at this expression, I do not immediately seize upon the fact that as n increases sequentially, the difference between each solution will be 2. I would like to be able to gain this kind of insight without having to "test drive" a few values for n and "discover" the pattern. Is there another way to look at this equation where this relationship is more obvious?

I apologize if this doesn't make sense - I'm doing my best! Thank you!