yes, the spring constants do change. bcoz since the length bcomes shorter more force is required to produce deformation in it.
u can determine the individual force constants as follows:
let L1 and L2 b the lengths of the 2 parts of spring such that L1>L2 and L1=nL2...(where n is an integer)
Now, if force constant of L2=k, then that of L1 will b k/n. If these 2 springs are connected in series then we get the original spring constant i.e K.
hence, 1/K=I/k+n/k
thus k= K(n+1) and k/n= K(1+1/n)
hope u got it...!