  Consider a sequence of positive integers of the form $ca^n-d$, $n\geq 1$,
where $a, c$ and $d$ are positive integers, $a>1$. For each $n\geq 1$, let
$S_n$ be the submonoid of $\mathbb N$ generated by $\mathbf s_j=ca^{n+j}-d$,
with $j\in\mathbb N$. We obtain a numerical semigroup $(1/e)S_n$ by dividing
every element of $S_n$ by $e=\gcd(S_n)$.
  We characterize the embedding dimension of $S_n$ and describe a method to
find the minimal generating set of $S_n$. We also show how to find the maximum
element of the Ap\'ery set ${\rm Ap}(S_n, \mathbf s_0)$, characterize the
elements of ${\rm Ap}(S_n, \mathbf s_0)$, and use these results to compute the
Frobenius number of the numerical semigroup $(1/e)S_n$, where $e=\gcd(S_n)$.
