The word hamartano is used once by Luke in Acts, where it is rendered as offend (Acts 25:8). The apostle Paul was defending himself against Festus, and says that he has not offended in any way — whether against the law of the Jews, or against the temple, or against Caesar. He was not standing before Festus because he had sinned against the civic or ecclesiastical orders.
Hamartia
is used eight times in Acts. The first is where Peter tells the crowd at Pentecost to repent and to be baptized for the remission of sins (2:38). In the next chapter Peter is preaching again, and he tells the people to repent so that their sins might be blotted out (3:19). When Peter is giving his courageous reply to the Sanhedrin, he says that Jesus was hanged on a tree in order to give repentance and forgiveness of sins to Israel (5:31).
When Stephen was about to die, he called upon the Lord not to lay the sin of murder to his attackers’ charge (7:6).
Peter, preaching to Cornelius and his household, said that whoever believed in Christ would receive remission of sin (10:43). Paul offers this promise as well — forgiveness of sins — in his message at Pisidian Antioch (13:38). And when he is preaching to his countrymen, giving his testimony, he recounts how Ananias told him to be baptized and wash away his sins (22:16). And when Paul is speaking before Agrippa, he recounts his commissioning as an apostle, in the course of which Jesus sent him to preach to the Gentiles that they might receive forgiveness of sins (26:18).
We can see from all this that apostolic preaching frequently included the topic of sin. The relative absence of sin in much of modern preaching is therefore a great mystery. Our theologians are still working on it.