Number-sequence questions ask you to predict what comes next or fill a missing value. The useful skill is not memorising a list of patterns; it is learning how to inspect the changes between terms. Begin with subtraction, then try multiplication or division, and only after that consider alternating or layered rules. Estimate the expected size of the next number so that arithmetic mistakes are easier to catch.
Start with consecutive differences
Subtract each term from the next. For 4, 9, 14, 19, the differences are+5, +5, +5, so the next term is 24. This is an arithmetic sequence: the same amount is added each time. Differences are a strong first check because they are quick and do not require you to guess the name of a pattern.
Try ratios when the numbers grow quickly
If subtraction does not reveal a fixed change, divide one term by the previous term when the division is exact or easy to recognise. In 3, 6, 12, 24, each value is doubled, so the next term is 48. A ratio pattern can also use a fixed fraction, such as halving, or a repeated multiplier followed by a simple adjustment. Always check more than one transition; a rule that fits only the last pair is not enough.
Look for alternating rules
Some sequences use two simple rules in turn. In 2, 5, 10, 13, 26, the operations alternate between “add 3” and “multiply by 2”: 2 + 3 = 5, 5 × 2 = 10, 10 + 3 = 13, and 13 × 2 = 26. The next operation is “add 3,” giving 29. If a sequence looks inconsistent, split it into odd-position and even-position terms and inspect each smaller sequence.
Recognise common families carefully
Squares and cubes are frequent because they are easy to explain. The sequence1, 4, 9, 16 contains 1², 2², 3², and 4², so the next term is 25. Triangular numbers grow by consecutive differences: 1, 3, 6, 10, 15 has differences +2, +3, +4, and +5. Familiar families are useful clues, but do not choose one just because it looks familiar. Confirm that it accounts for every term shown.
Worked example: a rule with an adjustment
Consider 2, 5, 11, 23. The differences are 3, 6, and 12, which double each time. Another description is “multiply by 2, then add 1”: 2 × 2 + 1 = 5, 5 × 2 + 1 = 11, and 11 × 2 + 1 = 23. Applying the same rule gives 23 × 2 + 1 = 47. The second description is useful because it shows exactly how to calculate the next term and makes the check easy.
When two rules seem possible
Short sequences can support more than one mathematical rule. In a practice question, prefer the simplest rule that fits every term and matches the answer choices. Do not invent a hidden condition solely to force one option. If the prompt provides a visual layout, row and column relationships may matter more than reading the numbers in one line. Write down the proposed rule and test it from the first transition to the last one.
Common mistakes and useful checks
- Checking only the first two terms: a rule must explain the whole sequence.
- Mixing operations: write the operation between every pair so you do not skip a step.
- Ignoring scale: an answer that is larger than expected may signal a multiplication error.
- Overfitting: prefer a short, repeatable rule over a custom formula for each term.
- Forgetting position: alternate rules often become clear when odd and even terms are separated.
Use explanations to build a reusable habit
After solving a sequence, explain the rule in one sentence and calculate the next term again without looking at your first result. That second pass checks both the method and the arithmetic. You can explore more category examples in the reasoning categories guide, read how the assessment works, or try a fresh randomized reasoning practice test. IQTestReal reports an Estimated IQ for this question set as an educational result, not a clinical or definitive measure of ability.
Key takeaway
Inspect differences first, ratios second, and alternating or familiar families next. The best sequence solution is the one you can state clearly and verify across every term—not the one that merely produces a plausible next number.