  In this article we introduce and study the lacunary arithmetic convergent
sequence space $AC_{\theta}$. Using the idea of strong Ces\`{a}ro summable
sequence and arithmetic convergence we define $AC_{\sigma_1}$ and study the
relations between $AC_{\theta}$ and $AC_{\sigma_1}$. Finally using modulus
function we define $AC_{\theta}(f)$ and study some interesting results.
