8, -4, 2, -1,

Question

What is the next number in the pattern

Answer 1

The goal is to determine how each of these numbers relates to the previous number. In this case, we are looking for a common ratio since this is a geometric sequence. The question we are asking ourselves is: "What can I multiply each number by to get the next number in my sequence?"

 

That is, what is the value of my common ratio r such that 8r = -4? 

Divide both sides by 8.

r = -4/8 = -1/2

 

Observe that 8 *(-1/2) = -4, -4*(-1/2) = 2, and 2*(-1/2) = -1 which means we have found a valid common ratio r= -1/2. Note that r is negative since every other value in our sequence switches from a positive to a negative value.

 

To find the next number in your sequence, solve:

(-1) *(-1/2) = 1/2.

So, the next number in your sequence is 1/2.

Answer 2

The ratio between 2 consecutive numbers is -½, so the next number is -1(-½) = ½