Since the first three terms of a geometric progression are k + 15,k and k - 12 respectively, 

we have this proportion


     = .


Cross multiply, simplify and find k


    (k-12)*(k+15) = k^2

     k^2 - 12k + 15k - 180 = k^2

           3k              = 180

            k              = 180/3 = 60.


The first three terms are  75, 60, 48.


The common dofference is  r =  =  = 0.8.


The sum to infinity is  S =  =  =  = 375.