A sequence is a list of numbers in order — each one is a term. A term-to-term rule is the single operation that takes you from one term to the next, the same step every time: maybe +3 each time, or \times 2 each time.

Once you know the rule, you can keep the sequence going forever — just apply it again. For 2,\ 5,\ 8,\ 11,\ \dots the rule is +3, so the next term is 11 + 3 = 14. This is the same equal-step idea as skip counting, now written as a rule. Naming the rule is a small step into turning words into algebra.

Press play: each term appears in turn, and the jump between consecutive terms is labelled with the rule. Watch how the same operation builds the whole sequence.

A first term and a term-to-term rule together pin down the whole sequence: start at the first term, then apply the rule again and again. Change either one and you get a different sequence.

Khan Academy extends arithmetic sequences here: