  We study some of the factorization invariants of the class of Puiseux monoids
generated by geometric sequences, and we compare and contrast them with the
known results for numerical monoids generated by arithmetic sequences. The
class we study consists of all atomic monoids of the form $S_r := \langle r^n
\mid n \in \mathbb{N}_0 \rangle,$ where $r$ is a positive rational. As the
atomic monoids $S_r$ are nicely generated, we are able to give detailed
descriptions of many of their factorization invariants. One distinguishing
characteristic of $S_r$ is that all its sets of lengths are arithmetic
sequences of the same distance, namely $|a-b|$, where $a,b \in \mathbb{N}$ are
such that $r = a/b$ and $\text{gcd}(a,b) = 1$. We prove this, and then use it
to study the elasticity and tameness of $S_r$.
