Finding a rule or a term from a numeric pattern
A pattern that changes by the same amount every step has one fixed rule connecting the term number to its value, however far along the pattern is asked about.
A worked example
The pattern 5, 9, 13, 17 changes by 4 every step. The 10th term is not found by continuing to count by 4 nine more times by hand. It is the first term plus nine steps of 4, since there are nine gaps between the first term and the tenth.
The mistake people actually make
The step size is the gap between consecutive terms, not the term values themselves, and the number of gaps to a given term is always one less than that term's position.