  Recently Ruckle \cite{RuckleArithmeticalSummability} introduced the theory of
arithmetical summability suggested by the sum $ \sum_{k|m}f(k) $ as $ k $
ranges over the divisors of $m$ including $ 1 $ and $ m .$ Following Ruckle
\cite{RuckleArithmeticalSummability} we construct the sequence space $ AS(G) $
and $ AC(G) $ of arithmetic summable and arithmetic convergent sequences in the
sense of geometric calculus and derive interesting results in the geometric
field.
