Maximal Rank Divisors on $\overline{\mathcal{M}}_{g,n}$

We compute the class of the effective divisors on $\overline{\mathcal{M}}_{g,n}$, which are set theoretically equal to the locus of moduli points $[C,p_1,\dots ,p_n]$ where $C$ lies on a quadric under the map given by the linear series $|K_C-p_1-\dots -p_n|$. Using this divisor class we show that the moduli spaces $\overline{\mathcal{M}}_{16,8}$ and $\overline{\mathcal{M}}_{17,8}$ are of general type. We also note that the divisor classes computed in the papers \cite{FV1} and \cite{FV2} can be used to show that $\overline{\mathcal{M}}_{12,10}$ is of general type as well.