Which term indicates a lively and brisk tempo?

The term "allegro" is used in musical terminology to designate a lively and brisk tempo. Traditionally, it suggests a pace that is fast and energetic, often associated with a sense of excitement or joy in the music. This term is commonly indicated in scores to guide performers in interpreting the speed and mood of a piece.

In contrast, "moderato" implies a moderate tempo that is neither fast nor slow, resulting in a more balanced and controlled expression. "Piano" refers to a dynamic level meaning "soft," which does not relate to tempo at all. "Adagio" indicates a slow and leisurely tempo, providing a stark contrast to the brisk nature of allegro. Thus, in this context, allegro accurately captures the essence of a lively and brisk tempo, making it the correct choice.