Algebraic Functions & Sequences (Periodic Remainder Heuristic)
GMAT glossary · Quantitative Reasoning
Definition
Periodic Remainder Heuristic for cyclic/recursive sequences , find cycle C, read remainder; or list until the cycle appears.
Algebraic Functions & Sequences (Periodic Remainder Heuristic) in plain English
Pull Algebraic Functions & Sequences (Periodic Remainder Heuristic) , also called Recursive Mapping , on cyclic or recursive patterns. Clues include A_n+k=A_n, a recursive rule, repeating pattern, or dependence on A_n-1 and A_n-2. Blueprint: find the repeating cycle length C, divide the target index by C, and look at the remainder to pick the term. If the sequence depends on A_n-1 and A_n-2, list individual values systematically until a fixed cycle emerges, then jump with the remainder. Why it beats the long way: writing out hundreds of terms invites arithmetic slips; the cycle remainder finishes in one step. Micro-example: a sequence repeats every 4 terms (cycle C = 4). For the 50th term, 50 div 4 = 12 remainder 2, so the answer is the 2nd term in the cycle.
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