Read, extend, and write explicit rules for arithmetic and geometric sequences.
A sequence is a list with addresses: term 1, term 2, term 3… Arithmetic sequences ADD the same difference each step (5, 8, 11, 14 — difference 3). Geometric sequences MULTIPLY by the same ratio (5, 10, 20, 40 — ratio 2). Same split as last week: adding vs multiplying.
The explicit rule jumps straight to any address without walking there. Arithmetic: aₙ = a₁ + (n − 1)d — start, plus n−1 hops of size d. Geometric: aₙ = a₁ · rⁿ⁻¹. Want term 50? No listing — just substitute n = 50.
Mastery looks like: They classify a sequence, write its explicit rule, and jump to a far term without listing.
Common stumbles: Using n instead of n − 1; assuming any increasing sequence is arithmetic without checking the move.