终于 = finally 最后 = at last 最后，我终于完成了作业。 at last，I finally finished my homework。 （verbose but correct sentence. actually u can just pick one of them~）

“终于”有代表自己心里在事情发生前有过一些想法。 “最后”一般是先后次序的意思。 你终于来了，他们都在等你。 别人都到了，她是最后来的。 我终于大学毕业了！ 他最后还是大学没毕业，因为好多考试没过。

最后：It means "at last" "in the end" "finally" When we use this word,it usually shows the reslut for one thing. 例如：我昨天去购物了，最后我什么也没买 eg:I went shopping yesterday,finally I don't buy anything 终于：It is similar to 最后。But this word used to express great emotion or desire for something you want or you are doing. 例如：我终于买到了冰激凌（表达了我对冰激凌的渴望） Finally I buy tht ice-cream(great desire for ice-cream) 我终于完成了作业（表达了一种辛苦的情绪,也许作业太多了;也许我要和我的朋友们踢球，所以急着先完成我的作业） Finally I finished homework(It show emotion I feel very hard,maybe there is too much homework;maybe I want to play football with my friends,so I finish my homework in a hurry at first)

谢谢你xuanying

终于：means Said the expected or desired things finally happened.Sometimes the don't want things happen eventually.Sentence: a vigorous patriotic war finally ended in smoke filled 最后：means finally，in the end,at last. After all the other time or order. But in the absence of time background is not set up! Typically on the order of the said is to point to in the most at the end of the.Sentence: a vigorous patriotic war finally ended in smoke filled。 i hope it can help you.