# 2, 4, 8,…

In precalc today, we started sequences and series. As an intro, I told them that I was thinking of a rule that the sequence 2, 4, 8,… followed. Their task was to figure out my rule by proposing a new sequence.

Popular suggestions were:

16, 32, 64,…

5, 10, 20,…

100, 200, 400,…

“Yes, those all fit my rule.”

“So your rule is multiplying by two.”

“No.”

“What? What about 3, 6, 12,…?”

“That also fits my rule.”

“So the rule is you’re doubling?”

“No, doubling is the same as multiplying by two, and–as I said–that’s not my rule.”

“Dividing by a half?”

“Dividing by a half is the same as doubling, which is the same as multiplying by two…which is not my rule.”

“I know. I was just trying to word it differently.”

Lolz. I can’t get enough of their cuteness some days.

They tried and they tried. They struggled and they struggled.

“I give up,” I would hear, only to be combatted with, “No! Not yet! Don’t tell us yet.”

{That’s when you know they’re hooked.}

I showed them this video, which uses the same sequence to highlight the fact that incorrect answers are sometimes more informative than correct ones

And then the kids figured out the rule.

If you’re curious, you can watch the video, too.