A number series question is a staple of IQ tests and aptitude tests: you get a handful of numbers and have to work out what comes next. Paste your number series below and this solver tells you the pattern and the next number instantly. Behind every solvable number series is a precise rule taken straight from the theory of sequences and series: a constant difference, a constant ratio, a recurrence, or a polynomial hiding in the differences.
This tool tries a list of such rules, in order from simplest to most elaborate, and reports the first one that reproduces every number you entered exactly — then uses it to predict the next term. It is built for practicing the number series questions found in IQ tests, but it works just as well for any arithmetic, geometric, or recurrence-based sequence.
Practice with example number series
Click any of these classic IQ test number series to load it into the solver above.
Which number series patterns does it recognize?
The solver tries the following rules, always preferring the simplest one that fits every entered number exactly. All arithmetic is done with exact fractions via Fraction.js, so it never loses precision to rounding.
- Constant, arithmetic, and polynomial sequences. The tool repeatedly takes differences of consecutive terms — the same construction as the discrete derivative of a sequence. If the terms themselves are constant, or the first differences are constant, that is an arithmetic sequence. If it takes a second, third, or fourth round of differencing to reach a constant row, the original sequence is a quadratic, cubic, or quartic polynomial in \(n\) — this is exactly how sequences like the perfect squares \(1,4,9,16,25,\ldots\) or the square pyramidal numbers \(1,5,14,30,55,\ldots\) are caught.
- Geometric sequences. Every step multiplies by the same fixed ratio, as in geometric sequences.
- Linear recurrences. Every term is a fixed multiple of the previous term plus a constant, \(a_{n+1}=r\cdot a_n+d\), generalizing both the arithmetic (\(r=1\)) and geometric (\(d=0\)) cases — see linear recurrence sequences.
- Fibonacci-like recurrences. Every term is a fixed linear combination of the two previous terms, \(a_n=p\cdot a_{n-1}+q\cdot a_{n-2}\), which reduces to the classic Fibonacci rule for \(p=q=1\).
- Factorial-style growth. The ratio between consecutive terms is not constant, but itself forms an arithmetic sequence — the signature of factorials, \(n!=1\cdot 2\cdot 3\cdots n\).
- Prime-driven sequences. The terms themselves, their differences, or their ratios are consecutive prime numbers.
- Periodic and alternating patterns. The values repeat with a short period, the differences cycle through a short repeating pattern (a "zigzag"), or the sequence alternates between two different operations applied in turn, such as multiply-then-subtract.
If none of these rules fits, the tool says so plainly instead of guessing — a genuine pattern must reproduce every number you typed, not just the first few.
Frequently asked questions
What is a number series in an IQ test?
A number series question gives you a short list of numbers that follow one consistent rule and asks you to find the number that comes next. IQ tests and aptitude tests use them to measure how quickly you can spot numerical patterns such as constant differences, constant ratios, or recurrences.
How do I solve a number series quickly?
Start with the simplest possible rule: check whether the difference between consecutive numbers is constant (arithmetic), then whether the ratio is constant (geometric). If neither works, look at the differences of the differences, check whether every term depends on the one or two before it, or check whether the numbers alternate between two operations. This solver automates exactly that checklist.
Why does it need at least four numbers?
Every rule the solver tries has a small number of free parameters (a difference, a ratio, two recurrence coefficients, ...). With too few numbers, many different rules would fit equally well, so the tool requires enough terms to actually confirm a pattern rather than merely guess one from too little evidence.
Can I enter negative numbers or fractions?
Yes. Negative numbers, decimals, and fractions like 1/2 are all accepted.
What if my number series isn't found?
The tool only reports a rule it can verify exactly against every number you entered. Some classic puzzle sequences use tricks outside this list, such as digit sums or alternating with a square root, and won't be recognized. Try entering a few more terms, or check the numbers for typos.