Let "a" be the first term and "d" be the common difference.
Now SX/SKX=X/2 (2a + (X-1)d)/KX/2(2a + (KX - 1)d)
=(2a + Xd- d)/(2aK + K²Xd - Kd)
=(2a + Xd- d)/[(2a-d)K + K²Xd]
=(2a + Xd- d)/k[(2a-d) + KXd]
Now since SX/SKX is independent of X then,
(2a - d )=0
or
d=2A