Number sequences for the NAPOLCOM exam: the seven rules a series can follow, and the checklist that finds which.
Number series items ask for the next term, or a missing term in the middle. They reward a fixed procedure more than any other item on the paper: write the differences, and if those do not settle it, run down a short list of rule families until one fits every term. This page gives the seven families, the checklist, and the discipline that stops the most common miss, which is a rule that fits the first two gaps and fails the third.
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- Worked examples
- 3
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Quick facts
- Ask
- The next term, or the missing term
- Rules
- 7 families cover nearly every item
- First move
- Write the differences
- Main trap
- Stopping at the first rule that fits two terms
- Time
- Under a minute once the checklist is automatic
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The seven rule families
Nearly every series on the exam is one of seven shapes, or two of them combined.
| Family | Example | The tell |
|---|---|---|
| Arithmetic (constant difference) | 4, 9, 14, 19, … | Differences all equal |
| Geometric (constant ratio) | 3, 6, 12, 24, … | Each term divides the next evenly |
| Growing differences | 2, 3, 5, 8, 12, … | Differences form their own arithmetic series |
| Squares, cubes, triangular | 1, 4, 9, 16, … / 1, 8, 27, … | Terms are perfect squares or cubes |
| Primes | 2, 3, 5, 7, 11, … | Every term has no divisors but 1 and itself |
| Alternating (two interleaved series) | 1, 10, 2, 20, 3, 30, … | Odd terms and even terms follow separate rules |
| Two-step (multiply then add) | 3, 7, 15, 31, … | Double plus one; differences double |
The checklist
Write the differences between consecutive terms. If they are constant, the series is arithmetic. If they are not, look at the ratios; if constant, geometric. If neither, look at the differences of the differences; if constant, growing differences. Then check whether the terms are squares, cubes or primes. Then split the series into odd-position and even-position terms and test each separately. Then try multiply-then-add. Stop at the first rule that fits every gap, and only then read the options.
The discipline is in 'every gap'. A rule that fits the first two differences and fails the third is the exam's favourite trap, and the wrong options are built from it.
Letter series
Some items use letters instead of numbers. Convert to positions in the alphabet (A = 1, B = 2, and so on) and the series becomes a number series with the same families. Skipping letters is an arithmetic series; alternating capitals and lowercase is two interleaved series.
Worked examples
These items are written specifically for this guide. The actual practice bank pulls from a separate pool of original NAPOLCOM-style items reviewed by passers.
Item 01
What comes next: 2, 3, 5, 8, 12, 17, blank?
- A21
- B22
- C23Correct
- D24
Explanation. Differences: 1, 2, 3, 4, 5. Growing differences; the next difference is 6, so 17 + 6 = 23. The differences form their own arithmetic series, which is the tell.Item 02
What comes next: 5, 11, 23, 47, blank?
- A71
- B89
- C94
- D95Correct
Explanation. Differences 6, 12, 24 double, which points to a two-step rule: each term is double the previous plus one (5×2+1 = 11, 11×2+1 = 23, 23×2+1 = 47, 47×2+1 = 95). C is double without the plus one; A is the arithmetic trap (adding 24 again).Item 03
Find the missing term: 4, 100, 6, 90, 8, blank, 10, 70.
- A60
- B75
- C80Correct
- D85
Explanation. Alternating. Odd positions: 4, 6, 8, 10 (add 2). Even positions: 100, 90, ?, 70 (subtract 10), so the missing term is 80. Splitting the series is the whole method; treating it as one sequence produces nothing.
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Study tactics that actually move the score
- 01
Write the differences first, every time. Half the items are settled there.
- 02
Run the whole checklist in the same order every time until it is automatic: differences, ratios, second differences, squares and primes, alternating, two-step.
- 03
Check the rule against every gap, not the first two. The wrong options are built from rules that fit two terms.
- 04
Convert letters to alphabet positions and treat them as numbers.
Frequently asked questions
How many series types are there?
Seven families cover nearly every item: arithmetic, geometric, growing differences, squares and cubes, primes, alternating, and two-step rules. Some items combine two.
What if none of the rules fits?
Split the series into odd and even positions and test each; most 'impossible' series are two interleaved simple ones. If that fails, choose the option closest to the trend and move on; the item is not worth three minutes.
Are letter series on the exam?
They appear. Convert each letter to its alphabet position and the same rule families apply.
Stop reading. Find your floor.
Forty questions across all four subtests, forty minutes, and a per-subject breakdown against the 80.00 pass mark.