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**"Find the next term"**

After studying more math, I've been conflicted about this type of assignment commonly given to high schoolers. In the sequence 1, 4, 9, 16, ____ find the next term.

On one hand, it's a good exercise and teaches pattern recognition. On the other though, it seems to go against a lot of math. 25 is the "obvious" choice, but is 25 any more correct than say, -43? Just because n^2 is A rule, and probably the "simplest" doesn't make it any more correct than any other rule. It seems to teach students to draw conclusions from incomplete information.

It DOES seem useful to teach kids pattern recognition and intuition. But is it really worth it? Or would there be a better way?