Write the gaps between terms, test simple multiplication or division, look for alternating rules, and verify your idea against every transition—not only the final two numbers.
Start with the differences between terms
For the sequence 4, 7, 10, 13, ?, subtract each term from the one after it. The differences are +3, +3 and +3, so the simplest rule is “add three.” The next term is 16.
Do not stop after checking one pair. A rule is useful only if it explains every visible transition. In 2, 5, 10, 17, ?, the differences are +3, +5 and +7. Those differences form their own pattern: consecutive odd numbers. The next difference is +9, which gives 26.
When first differences are not constant, write a second difference row. This turns a visual hunch into something you can test.
Check ratios when the values grow quickly
A sequence such as 3, 6, 12, 24, ? grows too quickly for a small fixed addition. Divide each term by the previous one: every ratio is 2. The next term is therefore 48.
Some puzzles combine multiplication and addition. For 2, 5, 11, 23, ?, each term is the previous term multiplied by 2, then increased by 1. Applying the same two-step rule gives 47.
Keep the order of operations visible in your notes. “Multiply by two, then add one” is not the same as “add one, then multiply by two.”
Test alternating and interleaved rules
| Position | Term | Change from previous term |
|---|---|---|
| 1 | 5 | — |
| 2 | 8 | +3 |
| 3 | 16 | ×2 |
| 4 | 19 | +3 |
| 5 | 38 | ×2 |
| 6 | 41 | +3 |
Here the operation alternates between +3 and ×2. Another common construction interleaves two independent sequences. In 2, 10, 4, 20, 6, 30, ?, the odd positions are 2, 4, 6, … while the even positions are 10, 20, 30, … . The seventh term belongs to the odd-position sequence, so it is 8.
If one rule almost works but repeatedly fails at every second term, split the odd and even positions before inventing a complicated formula.
Use the term position when the numbers look familiar
The position can be part of the rule. The sequence 1, 4, 9, 16, 25 contains square numbers: 1², 2², 3², 4² and 5². Triangular numbers, powers of two and Fibonacci-style sums also appear often, but a familiar-looking list is not proof by itself.
Label the positions 1, 2, 3 and so on, then state the connection clearly. If your explanation depends on an exception that appears nowhere in the question, look for a simpler rule first.
Verify the rule before choosing an answer
- Apply the proposed rule from the first term onward.
- Check every transition, including any alternating steps.
- Confirm that your next value matches the position being asked for.
- If two rules fit, prefer the simpler rule supported by the puzzle’s format and answer choices.
Math Riddles includes handcrafted number and logic puzzles with hints and solutions, so you can compare your reasoning after committing to an answer. Use the solo journey to practise at your own pace, or try the same question against a friend in a live 1v1 match.
Common questions
What should I check first in a number pattern?
Start with the differences between consecutive terms. If the values grow quickly, also check ratios. Then test alternating operations or separate odd and even positions.
Can a number sequence have more than one valid answer?
A short sequence can sometimes support several mathematical rules. Puzzle context, answer choices and the simplest rule that explains every term usually indicate the intended answer.
Published by Moocsoft, the independent studio behind Math Riddles. Examples and worksheets are illustrative. App features can vary by platform and version; see the store listing for current availability and in-app purchases.