I give a rigorous and mathematically well defined presentation of the Covariant and Gauge invariant theory of perturbations of a FLRW universe for 4th Order Gravity, where matter is described by a perfect fluid witha barotropic equation of state. The general perturbations equations are applied to a simple background solution of R^n gravity. Solutions of the perturbation equations have a number of interesting features. In particular there are values of n for which there is always a growing mode for the density contrast even if the universe undergoes an accelerated expansion. Such a behaviour does not occur in standard GR, where as soon as Dark Energy dominates the density contrast experiences an unrelenting decay. This peculiarity is sufficiently novel to warrant further investigation on 4th order gravity models.