Let the common difference be d. Then these equations are true,
so add all the left sides and all the right sides:

                y = 30-d
                x = 30-2d
                z = 30+d
                f = 30+2d
-------------------------
          y+x+z+f = 120

Notice that there are lots of different possibilities for x,y,z,f.

For example the arithmetic sequence could be 

10 20 30 40 50, which have sum 120 with d=10, or

20 25 30 35 40, which also have sum 120 with d=5, or 

54 42 30 18 6, which also have sum 120 with d=-12, or any of
an infinite number of possible arithmetic sequences.  But the
sum will always be 120.  That's interesting!

Edwin