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

Options

A. the Haplo-diplontic life cycle and it is seen in kelp
B. the Haplontic life cycle which is seen is Volvox and some species of Chlamydomonas
C. the Diplontic life cycle which is seen in seed-bearing plants.
D. the Haplo-diplontic life cycle which is seen in bryophytes and pteridophytes

Answer

To solve the question regarding the type of life cycle in which there is no free-living sporophyte and the dominant, photosynthetic phase is the free-living gametophyte, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Types of Life Cycles**:
- There are three main types of life cycles in plants: haplontic, diplontic, and haplodiplontic.
- Haplontic life cycle: Dominated by the haploid phase (gametophyte).
- Diplontic life cycle: Dominated by the diploid phase (sporophyte).
- Haplodiplontic life cycle: Alternates between haploid and diploid phases.

2. **Identify Key Characteristics of Haplontic Life Cycle**:
- In the haplontic life cycle, the only diploid stage is the zygote.
- The zygote undergoes meiosis to produce haploid spores.
- These spores develop into the gametophyte, which is the dominant and free-living phase.

3. **Analyze the Life Cycle Process**:
- The sporophyte (2n) is represented only by the zygote.
- The zygote undergoes meiosis to form haploid spores (n).
- The spores grow into a free-living gametophyte (n), which is photosynthetic.
- The gametophyte produces gametes through gametogenesis, which then fuse to form a new zygote.

4. **Identify Examples of Haplontic Life Cycle**:
- Common examples of organisms with a haplontic life cycle include certain algae like *Volvox*, *Spirogyra*, and some species of *Chlamydomonas*.

5. **Evaluate the Options Provided**:
- The question asks for the life cycle where there is no free-living sporophyte and the dominant phase is the gametophyte.
- Based on the characteristics and examples discussed, the correct answer is the haplontic life cycle.

### Conclusion:
The type of life cycle being described is the **haplontic life cycle**, where the dominant phase is the free-living gametophyte, and there is no free-living sporophyte.

---