The dominant generation in pteridophytes is the sporophytic generation.

Explanation:
Pteridophytes are a group of vascular plants that include ferns, horsetails, and clubmosses. They are characterized by the presence of true stems, leaves, and roots, as well as the ability to reproduce and spread through spores.

In the life cycle of pteridophytes, there are two distinct generations: the sporophytic generation and the gametophytic generation.

1. Sporophytic generation:
The sporophyte is the dominant phase in the life cycle of pteridophytes. It is the diploid (2n) phase that arises from the fusion of two gametes during fertilization. The sporophyte is responsible for the production of spores through meiosis. These spores are then released into the environment and can develop into gametophytes.

2. Gametophytic generation:
The gametophyte is the haploid (n) phase in the life cycle of pteridophytes. It develops from a spore and is responsible for producing gametes (sperm and eggs) through mitosis. The gametophyte is a small, independent plant-like structure that is usually photosynthetic. In pteridophytes, the gametophyte is typically short-lived and dependent on the sporophyte for nutrition.

The sporophytic generation in pteridophytes is considered dominant because it is larger, longer-lived, and more complex than the gametophytic generation. The sporophyte is the main plant body that carries out most of the plant's functions, such as photosynthesis, nutrient absorption, and reproduction. It is also the generation that is most visible and recognizable in pteridophytes.

In contrast, the gametophytic generation is relatively small and short-lived. It is mainly responsible for producing gametes that will fuse during fertilization to form the sporophyte. The gametophyte is often inconspicuous and dependent on the sporophyte for nutrition and support.

Therefore, the sporophytic generation is considered the dominant generation in pteridophytes due to its larger size, longer lifespan, and greater functional significance in the overall life cycle of these plants.