The correct sequence of stages of lifecycle of a silkworm is:

Egg, silkworm, pupa, silkmoth.

During its life cycle, the silkworm exhibits metamorphosis. This is the process where the young ones of an organism differ drastically from their adult forms in physical appearance. The silkworm starts its life as an egg, which changes into a crawling worm called the silkworm. It then weaves a covering around itself and gets shelled inside it, entering the next stage of life, called pupa. When, at maturity, the pupa breaks, an adult, winged, flying moth called the silkmoth comes out. This the final stage of silkworm's lifecycle.