The type of life-cycle in which there is no free-living sporophyte and the dominant, photosynthetic phase in such plants is the free-living gametophyte. We are talking about
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Solution
Haplontic life cycle
The gametophytic plant body is haploid which produces haploid gametes. These gametes fuse to produce diploid zygotes.
It germinates to produce a diploid sporophytic plant body which produces haploid spores. The spores germinate to produce haploid gametophytic plant bodies.
These two phases of gametophytes and sporophytes alternate with each other in the life cycle of the plant.
For example, algae like Volvox and Chlamydomonas have such a life cycle where the gametophyte is predominant and free-living and the sporophytic phase is not free living.
Final answer a) Haplontic life cycle shown in Volvox and some species of Chlamydomonas