We analyse the stellar populations in the host galaxies of 53 X-ray selected optically dull active galactic nuclei (AGN) at 0.34<z<1.07 with ultra-deep (m=26.5) optical medium-band (R~50) photometry from the Survey for High-z Absorption Red and Dead Sources (SHARDS). The spectral resolution of SHARDS allows us to consistently measure the strength of the 4000 AA break, Dn(4000), a reliable age indicator for stellar populations. We confirm that most X-ray selected moderate-luminosity AGN (L_X<10^44 erg/s) are hosted by massive galaxies (typically M*>10^10.5 M_sun) and that the observed fraction of galaxies hosting an AGN increases with the stellar mass. A careful selection of random control samples of inactive galaxies allows us to remove the stellar mass and redshift dependencies of the AGN fraction to explore trends with several stellar age indicators. We find no significant differences in the distribution of the rest-frame U-V colour for AGN hosts and inactive galaxies, in agreement with previous results. However, we find significantly shallower 4000 AA breaks in AGN hosts, indicative of younger stellar populations. With the help of a model-independent determination of the extinction, we obtain extinction-corrected U-V colours and light-weighted average stellar ages. We find that AGN hosts have younger stellar populations and higher extinction compared to inactive galaxies with the same stellar mass and at the same redshift. We find a highly significant excess of AGN hosts with Dn(4000)~1.4 and light weighted average stellar ages of 300-500 Myr, as well as a deficit of AGN in intrinsic red galaxies. We interpret failure in recognising these trends in previous studies as a consequence of the balancing effect in observed colours of the age-extinction degeneracy.
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