Final answer:
The correct order of bond strengths from weakest to strongest is: Covalent < Metallic < Ionic, where covalent bonds involve sharing electrons, metallic bonds feature delocalized electrons among metal cations, and ionic bonds are due to electrostatic attraction between ions.
Step-by-step explanation:
The sequence that represents the proper order of increasing bond strength is: Covalent < Metallic < Ionic. This order is based on general trends, since the actual strength can vary depending on the specific atoms and environment. Covalent bonds, which involve the sharing of electrons between atoms, generally have lower bond energy as compared to metallic and ionic bonds. Metallic bonds, which occur between metal atoms, are stronger due to the delocalization of electrons across a lattice of metal cations. Ionic bonds, formed between a metal and a nonmetal, are even stronger due to the electrostatic attraction between the ions.