Explicit and recursive sequences

Learn to read, generate and verify explicit and recursive sequences in precalculus. Practise substitution, starting indices, alternating signs, one-step recurrences and simple two-term recurrences. The set distinguishes a rule that defines a sequence from a short list that merely suggests a pattern.

Questions progress from direct term calculations to reindexing, testing equivalent definitions and finding where a proposed rule breaks down. Both single-select and multiselect formats include detailed explanations of the index arithmetic, initial conditions and common errors. Use exact arithmetic and work out terms on scratch paper before choosing an answer. No general recurrence theory or series formulas are required. These skills prepare you for discrete-change models and arithmetic and geometric sequences.