Final answer:
The genotype of the F1 generation is Rr, being the result of a cross between RR and rr. The expected phenotypic ratio in the F2 generation from a selfed F1 generation is 3:1, with three parts having smooth seed coats for every one part having wrinkled seed coats. If the F2 generation has 14,640 seeds, 3,660 of these seeds will have wrinkled seed coats.
Step-by-step explanation:
In the investigation of pea plants, if smooth seed coats (R) are dominant over wrinkled seed coats (r), and all the seeds obtained in the first filial generation had smooth seed coats, then the genotype of the F1 generation consists of heterozygous plants (Rr), since they are the result of crossing pure-breeding smooth (RR) with wrinkled (rr) seed coat plants.
When the F1 generation is selfed and the F2 generation is observed, the phenotypic ratio expected from a cross of heterozygotes (Rr x Rr) is 3:1, with 3 parts having smooth coats and 1 part having wrinkled seed coats. Using a Punnett square, we can see that the genotypic ratio in the F2 generation will be 1RR : 2Rr : 1rr, which corresponds to the expected 3:1 phenotypic ratio.
To calculate the number of seeds with wrinkled coats in the F2 generation, we apply the phenotypic ratio to the total number of seeds. If the total number of seeds in F2 generation is 14,640, then the number of seeds with wrinkled coats will be 1/4 of that number, as we expect a 3:1 ratio. Therefore, 14,640 seeds / 4 = 3,660 seeds with wrinkled coats.