Direct Linear Cycles
GMAT glossary · Playbook
Definition
Jump to a far term in an arithmetic sequence (or a fixed-difference cycle) using the common difference d and a modular slot map, instead of writing every term.
Direct Linear Cycles in plain English
Pull Direct Linear Cycles when a sequence advances by a fixed add or subtract each step, and you need a far term or the first return. Clues include Arithmetic sequence, common difference, every kth term, returns to start. Blueprint: Read the common difference d. Find the cycle length C if it repeats. Map index n to slot ((n-1) bmod C)+1. Why it beats the long way: Writing every term to a huge index wastes time once the cycle or closed form is clear. Micro-example: Sequence 3, 7, 11, 15, ldots with d = 4. The 20th term is 3 + 19 · 4 = 79. If values also cycle every 5 terms, map n with ((n-1) bmod 5)+1 instead of writing twenty lines.
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