The sergeant ____ the cadets by this time tomorrow.

Answer: Will be training (future continuous)

Explanation

The phrase "by this time tomorrow" refers to a specific point in the future. The future continuous tense ("will be training") describes an action that will be in progress at that future time, so it best fits the sentence.

• train — Base form; by itself it does not express the future time reference. It would need a future auxiliary (e.g., "will train") to indicate the future.

• trained — Past tense or past participle; refers to a completed action in the past, so it conflicts with the future time marker.

• Will be training — Correct. Future continuous indicates an action that will be ongoing at a specified future time.

• trains — Simple present (habitual); does not match a specific future time when an action will be in progress.

Example: "The sergeant will be training the cadets by this time tomorrow."