I have been attempting this question for the past 3 days with no luck:
The first four terms x, y, z, w of an arithmetic sequence satisfy x + y + z + w = 8 and xw + yz = -2. Find all possible values of x, y, z, w.
I know the key here is finding the difference between the terms but I am having a hard time figuring out how to find this. I tried:
y - x = d
z - y = d
w - z = d
I then substitue the second equation in to the first equation
y - x = z - y
I am actually not sure if this is the right method though because also I have thought about adding or subtracting all the equations together but I was not able to get a significant solution out of it. I just need a little guidance on how to find d the difference. Thanks for your time.