Pattern....refers to the reliable pattern found within a sequence. Students have been finding patterns since they were in pre-school. Some are AB patterns (red, green, red, green...) whereas other patterns are ABBABB type patterns (+3, -2, +3, -2).
Sequences...These are the number listed that follow a pattern. We usually label them as the "y" list and call them the OUTPUT list. ex: 3, 6, 9, 12...is a sequence. It follows the pattern of +3, where 3 is added to each number. Another sequence is 2, 7, 5, 10, 8, 13, 11... This sequence follows the pattern of +5, -2.
Arithmetic sequence has a consistent pattern where it has ONLY one pattern and it is applied to each of the numbers. An example would be 4, 7, 10, 13... The pattern is +3 or 3 is added to the previous term.
Term...this refers to the position a number is located within the list. We usually refer to this as the INPUT or "x" list. Think of it as ordinal numbers...1st, 2nd, 3rd,...
Rule...this is the function that determines which numbers will be generated within a sequence. Example would be... 3x + 1. If you put in a 1 (input)...3 x 1 = 3 +1 = 4. 4 is the output. If you put in a 2... 3x2=6 + 1 = 7...7 is the output. The sequences (y) that is created is 4, 7, 10....
