Are the following compounds aromatic?
Molecule 1, the cyclopentadienyl cation, is not aromatic. It only has 4 π electrons and does not fit the $4n+2$ rule.

Molecule 2, the cycloheptatrienyl cation (or tropylium cation), is aromatic; it has 6 π electrons and fits the $4n+2$ rule with $n=1$.

Molecule 3, azulene, is generally considered to be aromatic. It fits the $4n+2$ rule with $n=2$, and is often referred to as a "nonbenzenoid" aromatic compound. It can also be viewed as a fusion of two other aromatic units, the tropylium cation and the cyclopentadienyl anion.