Final answer:
The correct sequence of foliated rocks from least to most coarse is slate, phyllite, schist, and gneiss, reflecting an increase in metamorphic grade. The correct option is 4.
Step-by-step explanation:
The list of foliated rock types arranged according to increasing coarseness of texture is: slate, phyllite, schist, gneiss. This sequence reflects the progression of metamorphic grade from low to high, with slate being the finest-grained rock resulting from low-grade metamorphism of shale, to gneiss, which is a high-grade metamorphic rock characterized by its coarse-grained texture and distinct banding of light and dark minerals.
Metamorphic rocks are classified based on their texture, mineral content, and the conditions under which they were formed. Foliation, a key feature of these rocks, is a texture formed by parallel planes and alignment of minerals, often visible as bands in more coarsely textured rocks like gneiss.
Hence, Option 4 is correct.