To solve the problem, we need to examine the word that best fits the context. The phrase is "Despite his repeated failures, he remained __________ and continued working towards his goals." Let's analyze each option:
- Arrogant: This describes someone who is overly confident in a way that is often offensive. It does not fit the positive context of continuing to work despite failures.
- Indifferent: This suggests a lack of interest or concern. It does not align with the idea of continuing to work towards goals despite failure.
- Persistent: This term means continuing firmly in spite of difficulty. It is the most suitable choice as it directly relates to someone who keeps working towards their goals even after repeated failures.
- Hesitant: This implies being unsure or slow to act, which contradicts the notion of continued effort and determination.
Based on the analysis, the correct option is: persistent