How do you find a rule for a pattern

If it's the Nth Term rule then: 3, 6, 9, 12, 15 That's a pattern. You must first find what is the gap from 1 term to another. for example from 3 to 6 we know the gap is 3. Therefore it's known as + 3. You would have to write: 3n + 3 because if you look (The pattern is adding that's why we use + if it was substracting we would use the - in the middle) and at 6 the second term you can say 6 - 3 to show the previous Value which is 3 therefore you would have to write the Nth Term as 3n - 3