What’s next in sequence?

[ashndew]

What’s next?
1,-4,9,-16,.....

 

[tkhunny]

-2, why?

Please show your personal efforts.

1) There are infinitely many answers. Just find one and justify it.
3) Look for a pattern. Any pattern.

 

[Deleted member 4993]

What’s next?
1,-4,9,-16,.....

Any number can be next - depends on the "reading of the mind" of the person who made up the question . However, I would notice that the given sequence can be written as:

1², -2², 3², -4².......

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[pka]

What’s next? 1,-4,9,-16,.....

Do the given terms fit the pattern $a_n=(-1)^{n+1}n^2~?$
What is the next term?

 

[HallsofIvy]

I suspect that whoever set this problem expected you to look at "1, 4, 9, 16" and immediately think "Aha, squares!"