Number Series and Sequences
What you must understand
A number series question gives a list of numbers built by a rule and asks for the next term, a missing term, or a wrong term. Candidates need to recognise the common rule families: constant difference (arithmetic), constant ratio (geometric), alternating or two-interleaved series, differences that themselves grow by a fixed amount (second differences), squares and cubes with or without a small offset, and products or sums of the two previous terms.
Method
Compute first differences. If they are constant, you have an arithmetic series. If not, compute second differences; a constant second difference means a quadratic pattern. If differences look erratic, test ratios. If the series jumps up and down, suspect two interleaved series - check the odd positions and even positions separately.
Traps
- A series may combine two rules, for example alternate terms increase by 3 and by doubling.
- Signs may alternate, so differences are negative on alternate steps.
- One term may be deliberately wrong; find the rule that fits all but one number, then identify the outlier.
- Do not assume the simplest rule without checking it against every given term.
Worked example
Series: 2, 5, 11, 23, 47, ? Differences: 3, 6, 12, 24 - each difference doubles. The next difference is 48, so the answer is 47 + 48 = 95. Note the alternative view: each term is double the previous plus one (2×2+1=5, 5×2+1=11), which gives 47×2+1=95, confirming the result.