An example of an insect with gradual metamorphosis is:

Gradual metamorphosis, also known as hemimetabolism, is a type of insect development characterized by three life stages: egg, nymph, and adult. Insects that undergo gradual metamorphosis do not have a distinct pupal stage; instead, they emerge from the egg as nymphs, which resemble smaller versions of the adult and gradually develop into their final form through a series of molts.

Termites are a prime example of insects that exhibit gradual metamorphosis. They hatch from eggs into nymphs, which then grow and molt into workers, soldiers, or reproductive adults without undergoing a dramatic change in form usually seen in insects with complete metamorphosis (like butterflies and moths). This means that over time, the nymphs look increasingly like the adult termites, albeit at various developmental stages.

In contrast, adult butterflies and moths undergo complete metamorphosis, which includes distinct larval, pupal, and adult stages. Beetles, while they also belong to the complete metamorphosis category, experience a similar life cycle transition that is not gradual. Therefore, the correct choice, representing an insect with gradual metamorphosis, is clearly the termite.