last applies to something that comes at the end of a series but does not always imply that the series is completed or stopped.
last page of a book
last news we had of him
final applies to that which definitely closes a series, process, or progress.
final day of school
terminal may indicate a limit of extension, growth, or development.
terminal phase of a disease
ultimate implies the last degree or stage of a long process beyond which further progress or change is impossible.
the ultimate collapse of the system
Example Sentences
Adjective He was the last one out of the building. She succeeded on her last attempt. These are the last two books in the series. We are going to the beach for the last week of the summer. the last cookie in the jar She said she wouldn't marry him if he was the last man on earth. He was tragically killed during the last days of the war. I haven't seen her recently. The last time we met was at a party. Adverb He spoke last at the meeting. My horse was last in the race. She was first to arrive at the party and last to leave. I last saw him in the supermarket. They last went to the beach in June. This word was last used in the 17th century. See More
Word History
Etymology
Verb (1)
Middle English, from Old English lǣstan to last, follow; akin to Old English lāst footprint
Adverb
Middle English, from Old English latost, superlative of læt late
Noun (2)
Middle English, from Old English lǣste, from lāst footprint; akin to Old High German leist shoemaker's last, Latin lira furrow — more at learn