  The introduction of extra dimensions is an invaluable strategy for the
unification of gravity with other physical fields. Nevertheless, the matter in
hand is to be eventually reduced to the actual 4D spacetime. The Kaluza-Klein
theory is no exception to this well-known scheme. There are two procedures to
obtain the field equations from a higher dimensional action. One can either
take the variation of the effective action in that higher dimension and then
reduce the resulting equations or reduce the higher dimensional action to the
actual 4D and henceforward take the variations with respect to the constituent
fields of the theory. Here, for the case of a quadratic curvature model with a
Kaluza-Klein ansatz the field equations are obtained from the reduced action
and compatibility of these two procedures is discussed in detail.
