The pattern follows the rule: start with 1, then add consecutive even numbers (2, 4, 6, 8, 10...). 1 + 2 = 3, 3 + 4 = 7, 7 + 6 = 13, 13 + 8 = 21, and 21 + 10 = 31. This is a series where the difference increases by 2 at each step, creating a quadratic progression. The sequence can also be expressed as n² - n + 1 for the nth term.