active 指有活动能力，强调与消极或休止相反的积极活动状态。
energetic 提精力充沛、奋力从事某事业。
vigorous 指不仅表现积极、有生气，而且固有精力和活力十分旺盛。
brisk 指动作敏捷、充满活力、轻快活泼地从事某项工作或活动。
lively 侧重支轮船快，机智，有生气。
参考例句
1. He gave us a lively and interesting math. lesson. 他给我们上了一节生动、有趣的数学课。
2. Ah! Diving feeling I seem to feel that they are a lively and cute fish! 啊！潜水的感觉真爽，我似乎觉得自己就是一只活泼可爱的鱼！
3. The concert has a serious purpose, but it is also a celebration. There is lively entertainment from Broadway hits to jazz and country music. 音乐会有着严肃的目的，但也是一种庆典。有现场的百老汇走红的演出，也有爵士乐或者乡村音乐。
英英解释
adj.
1. full of life and energy
2. full of zest or vigor
3. quick and energetic
4. elastic; rebounds readily
5. filled with events or activity
6. full of spirit
7. characterized by energetic activity
