Lacunary Arithmetic convergence

In this article we introduce and study the lacunary arithmetic convergent sequence space $A{C}_{\theta }$. Using the idea of strong Ces`{a}ro summable sequence and arithmetic convergence we define $A{C}_{{\sigma }_1}$ and study the relations between $A{C}_{\theta }$ and $A{C}_{{\sigma }_1}$. Finally using modulus function we define $A{C}_{\theta }(f)$ and study some interesting results.