A sequence follows one rule the whole way along, and once you know it you can jump straight to a term far out of reach. These free printable worksheets ask for the rule — the common difference or ratio — and for a term too far to count to.
Kid stuck on one? You don’t just get the sheet.
The answer key prints on a separate page.
The rule is one subtraction or one division of two neighbouring terms: 5, 12, 19, 26 climbs by 7 every time, and 3, 6, 12, 24 doubles. Finding it is where every other question starts, so the common-difference and common-ratio sheets practise just that.
The nth-term sheets then ask for the 20th term, or the 8th — far enough that writing the sequence out is the long way round. That is the whole point of the formula: the first term is already there, so you add the step (n − 1) times, not n. The (n − 1) is the single most common slip, and every step-by-step walk here says it out loud.
One question from this sheet, worked through a step at a time.
−5, −3, −1, 1, … — the 10th term