What are the next three terms of the arithmetic series:?

It's an arithmetic series so that means there is a common difference.

What do you need to do to go from 4 to -32?
--> Subtract 36
So the common difference is -36

You can verify this with the next term which would be found by subtracting another 36.
-32 - 36 = -68

All you have to do is to subtract 36 each time to find the next 3 terms.
a[4] = a[3] - 36
= -68 - 36
= -104

I can already see that C will be the answer.

Answer:C) -104, -140, -176

What are the next three terms of the arithmetic series:
40, 4, -32, -68, ...
C -104, -140, -176

check for common difference 
4 -40 =-36  
-32- 4  = -36 
-68- (-32) = -36 
so its' -36   
next terms 
-68+ (-36)  = -104 
-104 -36 = -140  
-140 -36  = -176 

so it can only be 
Answer :  (c)  -104, -140, -176