When I was giving my lecture to on phylogeny and tetraploidies, I found out not everyone knows why bananas don’t have seeds.
The reason the bananas we eat don’t have seeds is that they are all sterile. A long time ago the Cavendish bananas first came into being when a tetraploid banana (that is a plant that has four copies of every chromosome instead of the normal two) mated with a normal diploid banana. The result, a banana with three copies of every chromosome couldn’t mate or produce seeds. One of the steps in making reproductive cells (the analog of human sperm and egg cells) is the even dividing of a plant’s chromosomes into two reproductive cells.* Normal diploid cells can easily divide into two cells (one copy of each chromosome in each cell), tetraploid plants can divide the same way (two copies of each chromosome in each cell). Hexaploid, three copies in each and so on. Odd numbers of chromosomes don’t work. The plants can’t successfully make the cells it needs to reproduce, if it can’t reproduce it can’t make seeds, and that is why bananas (or seedless watermelons) don’t have seeds.