We present the Covariant and Gauge Invariant theory of scalar perturbations of a Friedmann-Lemaître-Robertson-Walker universe for Fourth Order Gravity, where the matter is described by a perfect fluid with a barotropic equation of state. The general perturbation equations are applied to a simple background solution of Rn gravity and we obtain exact solutions of the perturbation equations for scales much bigger than the Hubble radius. These solutions have a number of interesting features. In particular we find that for all values of n there is always a growing mode for the density contrast, even if the universe is in a state of accelerated expansion. Such a behavior does not occur in standard General Relativity, where as soon as Dark Energy dominates, the density contrast experiences an unrelenting decay. Consequently, this peculiarity in the framework of higher order gravity model is sufficently novel to warrant further investigation.