Question

Make a conjecture about the next item in the sequence 1, -4, 9, -16

Answer 1

The  absolute values of each term are a  sequence of  perfect squares  and the sign alternates  so the next term would be 5^2 = 25 answer.

Answer 2

To get -4 from 1, we must either subtract 5 from 1 or mult. 1 by -4. Unfortunately subtracting 5 from -4 does not result in 9, and mult -4 by -4 does not result in -16. So neither "works" in predicting the next term.

Can you think of any other experiments to do that would help you discover the pattern 1, -4, 9, -16?