Number Logic — Sequence / Find the Pattern

A no-calculator aptitude section: ~25–26 number sequences in 25 minutes, infer the rule and supply the next term. Scoring is +1 correct / −1 wrong. Most candidates report needing ~15 correct to pass comfortably. Requirements About 25–26 sequences in ~25 minutes (some QT sittings report ~22). Single-answer; on most platforms you can revisit within the section. No calculator — arithmetic must be done on paper / mentally. Scoring is +1 for correct, −1 for wrong, so skip rather than guess wildly. Candidates consistently say ~15 correct is "safe" and ~18 is comfortable. Rules span: constant/alternating differences, second-order differences, interleaved odd/even-position rules, multiplicative steps, ratios/fractions, Fibonacci-like recurrences (a_n = 2·a_{n-1} + a_{n-2}), prime lists, and "fourth term = product of previous three" patterns. Examples Reported sequences (bold = reported answer): 19 18 20 60 15 14 16 → 48 3 7 13 19 29 37 → 43 58 8 50 10 40 15 → 25 -12 -11 -7 2 18 43 → 79 12 28 36 84 88 168 → ? 1 3/2 4 9½ 23 55½ → next via a_n = 2·a_{n-1} + a_{n-2} 7 6 8 24 6 5 7 → repeating ×/+ cycle (−1, +2, ×3, ÷4) 5 3 8 9 11 27 → odd positions +3, even positions ×3 3 1 2 6 12 144 → ? 1 2 5 11 26 59 → ? 2 1 3 4 7 11 18 → ? Notes Many sequences hide interleaved rules — treat odd-indexed and even-indexed terms as separate progressions before assuming a single rule. Fractions appearing only in the final term are a strong hint the recurrence multiplies by a non-integer or divides — work backward from the fraction. First pass: solve everything obvious in ~30 seconds each and skip anything that doesn't yield; circle back with remaining time rather than stalling. Preparation Drill sequence/series aptitude sets (e.g. TraderMath / aptitude-test-prep style); build reflexes for first- and second-difference scanning and ratio scanning. Practice the interleaved-rule check explicitly: split into even/odd index streams on every sequence you can't crack in one pass. Rehearse mental arithmetic with fractions and small multiplications so the no-calculator constraint isn't the bottleneck.