Actually, I wanted patterns that grow by the same amount every time.
We might call these linear patterns. At least that's what I was hoping for.
And for the most part that's what I got.
Q: "Hey Mr. Rowinsky, we couldn't seem to find the algebraic expression for this one."
A: "Umm, ya, those aren't, ummm linear. They don't grow by the same amount. What you've discovered is a pattern that grows by an amount that grows. That's advanced."
Q: "But do these have an algebra expression we can use?"
A: "Good question!" as I think to myself, 'not one that I know off-hand.'
Awkward smiles and blank stares
I rush to Wolfram Alpha to find the solution. And Wolfram Alpha came through.
Some initial thoughts:
1) Sometimes students take it to the next level without any help
2) Sometimes I need help with the next level
3) We live in a world where we shouldn't fear 1 or 2.