Number Series and Pattern Recognition
Number series questions ask you to infer the rule that generates a sequence and then continue it or find the missing term. Start by checking differences between consecutive terms: constant differences signal an arithmetic series, while differences that grow steadily signal a second-order pattern (look at the differences of the differences). If differences are erratic, check ratios for a geometric series, then look for alternating patterns where odd and even positions follow separate rules. Also consider squares, cubes, primes, and simple recurrences such as each term being the sum of the two before it.
Common traps: a sequence may switch rules partway through; a single outlier may be the term you are asked to identify; and answer choices often include values produced by applying the wrong operation (adding instead of multiplying). Always test your rule against every given term, not just the first two, before choosing.
Worked example: 3, 6, 11, 18, 27, ? The differences are 3, 5, 7, 9 - increasing by 2 each time. The next difference is 11, so the answer is 38. Rule of thumb: if first differences form a clean pattern, trust it; if not, go one level deeper before guessing.