\begin{abstract} Let $R$ be a commutative Noetherian ring, $I$ and $J$ two ideals of $R$, and $M$ a finitely generated $R$-module. We prove that $\Ext_R^i(R/I,H_{I,J}^t(M))$ is finitely generated for $i=0,1$ where $t=\inf\{i\in{\mathbb{N}_0}: H_{I,J}^i(M)$ is not finitely generated$\}$. Also, we prove that $H_{I+J}^i(H_{I,J}^t(M))$ is Artinian when $\Dim R/{I+J}=0$ and $i=0,1$. \end{abstract}
