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

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?