Dr syphilis clear question exposure april 1 then taken z pak 3 days course 500mg per day may 30 ,31, june 1 test rpr neg at june 2, 54 days but then thought to retest so took again after 2 more months august around 120 days rpr neg so its conclusive?

The test result is conclusive: you do not have syphilis. However, the negative result cannot tell whether you were never infected (which is most likely) or acquired early infection that was cured by azithromycin before it had a chance to create a positive blood test. You will never know for sure, but so what? It doesn't matter now.

Syphilis window period: https://www.e7health.com/post/155/std-test-window-when-should-i-get-tested/#:~:text=The%20average%20window%20period%20or,it%20develops%20in%20three%20stages. https://www.cdc.gov/std/syphilis/stdfact-syphilis-detailed.htm