Are there well-specified formal languages that are not regular? Given a finite alphabet, there are well-specified formal
  languages that can not be recognized by regular expressions, FSAs or regular
  grammars True/False


I am studying for my exam and I am unsure about this question. From my understanding, you generate formal languages from regex, FSA. For i.e. for a* our formal language will be 

empty,a,aa,aaa etc. 

So I can identify if a formal language can be described by a regex, but not sure if that is always the case. Could somebody please help me with this?
There are indeed well-specified formal languages that cannot be represented by regular expressions, even on a one-letter alphabet. Examples include $\{a^{n^2} \mid n &gt; 0\}$ and $\{a^p \mid p \text{ is a prime number}\}$.