Step 1: Understand the concept of inner transition elements.
Inner transition elements are divided into two series:
First inner transition series – Lanthanides (4f block)
Second inner transition series – Actinides (5f block)
Step 2: Identify the given elements.
Samarium (Sm), Lutetium (Lu), and Dysprosium (Dy) belong to the lanthanide series.
Americium (Am) belongs to the actinide series.
Step 3: Match with the second inner transition series.
Since the second inner transition series corresponds to actinides, Americium is the correct choice.
Step 4: Conclusion.
Americium belongs to the second inner transition series.