What is the next number in the pattern?
1, -4, 9, -16

Question

What is the next number in the pattern? 
1, -4, 9, -16

tkhunny · Answer

There are infinitely many answers to this question.  Just pick one.

anonymous · Answer

The next number in the sequence @tkhunny

tkhunny · Answer

Right.  Infinitely many.  You haven't picked one, yet.  Go ahead.  It doesn't matter what it is.

anonymous · Answer

The number after -16 @tkhunny

tkhunny · Answer

Why are you not picking a number?  Just pick one.  Seriously, any number will do.  Go!

anonymous · Answer

5 @tkhunny

anonymous · Answer

It must go with the pattern. @kenna_098

tkhunny · Answer

Perfect.  That is a perfectly acceptable "next number"

There isn't A pattern.  There are infinitely many patterns.

tkhunny · Answer

Sequence the values 1, 2, 3, 4, 5 <== It's just the number sequence of the now 5 numbers.

$n_{1} = 1$
$n_{2} = -4$
$n_{3} = 9$
$n_{4} = -16$
$n_{5} = 5$

$f(n) = (1/6)\left(35x^{4} - 406x^{3} + 1615x^{2} - 2558x + 1320\right)$

Try it out.

tkhunny · Answer

Okay, someone may want you to pick what THEY have imagined.  The author of the problem may have something in particular in mind.  It is very arbitrary to ask such a question, but it is rather common.

$n_{1} = 1 = 1^{2}$
$n_{2} = 4 = 2^{2}$
$n_{2} = 9 = 3^{2}$
$n_{2} = 16 = 4^{2}$
$n_{2} = 25 = 5^{2}$

Not quite.  How shall we fix it?

anonymous · Answer

I don't know but there are answer choices.... -35, -25, 25, 35 @tkhunny

tkhunny · Answer

Sorry., all those little '2's should be 1, 2, 3, 4, 5, not 1, 2, 2, 2, 2

What do you think?  Did that last pattern look close?

tkhunny · Answer

$n_{1} = 1 = 1^{2}$
$n_{2} = 4 = 2^{2}$
$n_{3} = 9 = 3^{2}$
$n_{4} = 16 = 4^{2}$
$n_{5} = 25 = 5^{2}$

How is this different from your sequence?

anonymous · Answer

Oh i get it now.... thank you. You had me lost there for a second. @tkhunny

tkhunny · Answer

The are all squares of integers.
We just need a mechanism to change the sign each time.

Show your teacher the one where 5 is the next number.  Tell me what he/she says about it.

anonymous · Answer

Okay, Ill keep you posted!! Thanks for the help. @tkhunny

tkhunny · Answer

Some people think there is a  "simplest" or "best" or "most obvious".  Those who believe this are misguided.  If you were in my class and you said "5", I would ask you to justify that answer.  If you could, you wild get full credit.  If you could not, you would get no credit.