1st term = x+1, 
2nd term = 3x-2, 
and 
3rd term = 4x+5

In order to form an arithmetic sequence, this must be true:

        

      (3x-2)-(x+1) = (4x+5)-(3x-2)
         
You solve that and get x=10.
So

1st term = x+1 = 10+1 = 11 
2nd term = 3x-2 = 3(10)-2 = 30-2 = 28 
and 
3rd term = 4x+5 = 4(10)+5 = 40+5 = 45

So the series is 11, 28, and 45.

Checking in

         

            28 - 11 = 45 - 28
                 17 = 17.

So the answer is correct with a common difference of d=17.

Edwin