A sequence is a list with a rule, and this chapter runs on exactly two rules. If each term is made by adding the same amount — 3, 7, 11, 15 — the sequence is arithmetic, and the fixed step is the common difference $d$. If each term is made by multiplying by the same amount — 3, 6, 12, 24 — it is geometric, and the fixed multiplier is the common ratio $r$. Terms are named $t_1, t_2, t_3, \ldots$ — read t-one, t-two — with $t_n$ (t-sub-n) standing for whichever term you want.

The sorting test costs five seconds and never lies. Subtract neighbours: a constant answer means arithmetic. Divide neighbours: a constant answer means geometric. Money runs on both — a paycheque saved every month climbs arithmetically, interest left to compound climbs geometrically — which is why this chapter ends at the bank.