Answer:
Pattern: Multiply by -0.5 (or divide by 2 and multiply by 1)
Next number: -5
Explanation:
Let's look at the list of numbers so far, and see what patterns we can see:
160, -80, 40, -20, 10
We are looking for an operation (eg. multiplication, division, subtraction, or addition by a certain number) that in each case, changes any number in the list to the number following it.
Immediately one thing we might notice is we start with a positive number, then negative, then back to positive, and then back to negative, and so on. So since we are going over and back between positive and negative, we can conclude that our operation involves multiplying by a negative number.
Now that we've accounted for the signs, let's look at the numbers themselves.
The first numbers are 160 and then 80. The obvious potential operations from 160 to 80 are minus 80, or divide by two.
Then we have 80 and 40. Do either of our potential operations from above work here? Well minus 80 doesn't work, as we would get zero not 40. But dividing by two works.
Looking at 40 and 20, and then 20 and 10, we can see that dividing by two works there too!
So the operation for this pattern is divide by 2, and multiply by -1. Dividing by 2 is the same as multiplying by 0.5, so the simplist way to describe the pattern here is each number in the list is multiplied by -0.5 to get to the next number.
Use this to find next number: 10 x -0.5 = -5