Step 1: Identifying the first element of the rare earth series.
The rare earth elements include the lanthanides and actinides. The first element of the lanthanide series is Cerium.
Step 2: Explanation of the options.
- (1) Cerium: Cerium is the first element in the lanthanide series of rare earth elements.
- (2) Cesium: Cesium is an alkali metal, not a rare earth metal.
- (3) Lanthanide: Lanthanide refers to the series of elements and not a specific element.
- (4) Actinide: Actinide is a series of elements, but cerium is part of the lanthanide series, not the actinide series.
Step 3: Conclusion.
The correct answer is (1) Cerium.