There's no pattern for "tithing" at all, because Paul was not asking for a tithe.
When Paul met with the apostles in Jerusalem for the first time, they endorsed his ministry to the Gentiles, as they continued to minister to Jewish Christians in Jerusalem and Palestine. As he writes to the Galatians, "they asked us to remember the poor, the very thing I was eager to do" (Gal. 2:10).
Paul spent much of his time as a missionary taking up a collection amongst the European believers for the relief of poor Christians in Jerusalem. When he wrote to the Romans, he was conveying such a gift from Macedonia and Achaia (Rom. 16:26). In fact, it was probably his insistence on delivering that very gift in person, that resulted in his arrest in Jerusalem (Acts 21:27ff) - although the prophet Agabus warned him that he would be arrested, Paul was determined to accept the risk (21:13-14).
Paul's teaching to the Corinthians on giving is based on this same charitable gift. Paul was not advocating for a tithe - since the Corinthians were Gentiles living in Greece, they were not subject to the Law of Moses. He was instructing the Corinthians how to expedite a collection for the relief of the Hebrew Christians.
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On the first day of every week - because that is when the church met for worship.
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each of you is to put something aside and store it up, as he may prosper - Giving was to be tied to income. Notice that Paul does not call the gift a "tithe" (which literally means one-tenth), or instruct the Corinthians to give a specific proportion of their wealth. He simply says to give as they had prospered. Those whom God gives more, should give back more.
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so that there will be no collecting when I come - in other words, don't wait until Paul is there to pass the hat.
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when I arrive, I will send those whom you accredit by letter to carry your gift to Jerusalem - It was customary in that day, when sending an emissary, to supply them with letters of recommendation. This was a letter written by the sender to the receiver, and it attested to the character of the emissary as well as his ability to perform the function for which he was sent - that the emissary was, in fact, accredited to speak for the sender. Paul adds that if necessary, he would accompany them personally. (Presumably, his own credentials were above question in Jerusalem.)
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Other passages (e.g. 2 Cor. 8-9) have more to say about giving, but this passage in particular tells us this:
- Giving is regular.
- Giving is related to income.
- Giving should be planned.
- The stewards of the gift should be trustworthy.