Question 1203220
<font color=black size=3>
If the terms are odd numbers alternating in sign, then we extend the sequence to get: -1, 3, -5, <font color=red>7, -9, 11, -13, 15, ...</font>
The formula for the nth term would be {{{a[n] = (-1)^(n)*(2n-1)}}} where n starts at n = 1
The 2n-1 portion is always odd when n is an integer.
The (-1)^n portion alternates the sign from positive to negative, or vice versa. 


Again this assumes the pattern extends like that.


---------------------------------------------


Another possibility is this sequence: -1, 3, -5, <font color=red>-25, -57, -101, -157, -225, ...</font>
The terms in red are determined from the formula {{{a[n] = -6n^2 + 22n - 17}}}
I used interpolation to find this formula.


For instance, plug in n = 1 to determine the 1st term
{{{a[n] = -6n^2 + 22n - 17}}}
{{{a[1] = -6*1^2 + 22*1 - 17}}}
{{{a[1] = -6*1 + 22*1 - 17}}}
{{{a[1] = -6 + 22 - 17}}}
{{{a[1] = 16 - 17}}}
{{{a[1] = -1}}}
Repeat for n = 2 to arrive at {{{a[2] = 3}}} and so on.


---------------------------------------------


Here's another possibility


The starting sequence is -1, 3, -5
The gap from -1 to 3 is +4
The gap from 3 to -5 is -8


Then the jump from +4 to -8 is "times -2"
If that "times -2" pattern holds up, then the next gap could be +16 because -2*(-8) = 16


So -5 + 16 = 11 could be the next term


Then the next gap could be -2*16 = -32
So 11 + (-32) = -21


Then the next gap could be -2*(-32) = 64
So -21 + 64 = 43


-1, 3, -5, <font color=red>11, -21, 43, ...</font>


---------------------------------------------


As the other tutors have mentioned, questions that ask about the next term in a sequence tend to be too vague. 
If the teacher mentioned something like "the sequence is arithmetic" or "the sequence is geometric", then it would narrow things down to be able to determine the next term(s).


In this current state, it is not enough information to simply state "-1, 3, -5" and ask for the next term(s).


Further Reading:
<a href="https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1195799.html">https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1195799.html</a>
</font>