size of the collection of all formulas under a countable language is $\aleph_0$

Question

Let $L$ be a countable language.

I want to show the size of the collection of all $L$-formulas is precisely $\aleph_0$.

Attempt:

I know by definition an atomic $L$-formula obtained by equating or relating $L$-terms.

So I want to show the the size of the collection of $L$-terms is countable, where the $L$-terms can be a variable, a constant, or function of other $L$-terms.

But now I'm not sure what to do next.

Thanks in advance!