I've essentially worked my way through understanding arithmetic and geometric sequences, but my assignment expects me to figure out sequences that are neither of those things, and I can't find any references online on how to start with these.

For example: "Find the general term in simplest form for the sequence: 2, 1, -4, 7, -10, 13, -16

I was told that there were no available formulas and i was to just experiment with it until i got something.

When looking through the text, I was able to find a relatable sequence that helped make sense of the initial 2 positives and alternating - +'s.

The example being: a(n)=-1^n-1(3n-5)

But, when trying to reverse engineer this into something that'd fit my question I'm completely stumped as I can't find anything that'll give me that jump from 1 to 3... The |3| added value is there, but this is just one example of questions that seem to be coming out of the left-field in relation to the rest of the work and reading i've done leading up to this point. I think the problem is that I've been depending on formulas that the book gave me (Mainly have just been doing graphing, function, models, equations, inequalities, etc. up to this point which I can't relate to any of this stuff)

Does anyone have any suggestions for material to read up on that'll help me with the logic behind these kinds of questions?

Kind of a mouthful, but I'd appreciate any input.

Thanks!