We consider the product sequences of the sequences $(\Psi _{n}(\mathbf P))$, $(\Phi _{n}(\mathbf P))$, and $(\overline{\Omega}_{n}(\mathbf P))$ ($n\in \mathbb N$) of values of the translated division polynomials of an elliptic curve $E/K $ evaluated at a point $\mathbf P\in $ $E(K)^{2}$. We prove that thesesequences are purely periodic when $K$ is a finite field. Then we use $p$-adic properties of these sequences to obtain $p$-adic convergence ofproduct of the Somos $4$ and Somos $5$ sequences.