Why Did Paul Write to the Romans?

Why would Paul write to people he didn’t know, his letter sent to a place he had never visited?
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Since Paul said he didn’t build on another person’s foundation (Romans 15:20), we might think he would leave Rome to others. Something must have made that area an important exception to the rule.
Some Christians who fled Jerusalem settled in Rome.
Usually, people will leave their comfort zones only after it has become sufficiently uncomfortable. Without the persecution the followed the Day of Pentecost, few Christians would leave family and friends, solely to obey Jesus and spread the good news to Jerusalem, Judea, Samaria, and the uttermost parts of the earth (Acts 1:8).
Rome was a major center for commerce and social prosperity, so it was an ideal place where Christians could find work and build a new home.
The Roman Christians needed support.
When people in the Jerusalem church settled in Rome, we would expect them to want their leaders to visit them. If Peter visited Rome (we can’t prove he didn’t), his speaking Aramaic, not Greek, would have hindered his ability to reach out to the community.
Paul’s education and language skills made him a much more capable minister to the citizens of Rome, both with Jewish and non-Jewish backgrounds.
Peter speaks highly of Paul (2 Peter 3:15), so we can’t rule out the possibility that Peter visited Jerusalem, then encouraged Paul to go.
Paul had Christian friends from Rome.
In the last chapter of Romans, Paul sends greetings from a long list of names that would have the most meaning if they were known to those reading his letter. We know Priscilla and Aquila were from Rome (Acts 18:2). At least some of the others were either from there or had visited there.
Friends of Paul who had a burden for the Romans would have encouraged him to at least write if he couldn’t go there.
Paul eagerly anticipated going to Rome.
By the Spirit, the encouragement of friends, or perhaps an invitation from Rome, Paul had a burden for Christians there, continually mentioning them in his prayers (Romans 1:9). Whatever the reason, at the time he wrote his letter, he had a deep longing to minister in Rome (Romans 1:10).
The Holy Spirit directed him.
We may plan our journeys, but God orders our steps (Proverbs 16:9). There were times when Paul planned to go one way, but God took him in a different direction. Even under specific goals, he still had to follow the Lord one step at a time.
When Paul was directed by the Spirit toward Jerusalem, he may have wondered if he would ever go to Rome (Acts 21:10–13). Yet it was that trip that led to his arrest and tumultuous journey that took him to ministry in Rome for at least two years (Acts 28:30).