Quick answer
A number sequence is classified as arithmetic (constant difference) or geometric (constant ratio). The sequence 2, 4, 6, 8 is arithmetic with d = 2, and its next terms are 10, 12 and 14.
Enter at least three terms separated by commas. The calculator identifies the pattern and gives the next terms.
Related tools: Arithmetic Sequence Calculator: nth term and sum of an arithmetic sequence. Geometric Sequence Calculator: nth term and sum of a geometric sequence. Slope Calculator: Slope, angle, distance and line equation through two points.
How to use the Number Sequence Calculator
- Type sequence, for example 2, 4, 6, 8.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Sequence | Text, such as 2, 4, 6, 8 | — |
Formula and method
Formula
arithmetic: constant difference; geometric: constant ratio
IEEE-754 double precision; shown to at most 6 decimal places.
Checks differences then ratios (tolerance 1e-9); other sequences are reported as unrecognised.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Sequence = 2, 4, 6, 8.
| Result | Value |
|---|---|
| Pattern | Arithmetic (d = 2) |
| Next terms | 10, 12, 14 |
Example 2
Inputs: Sequence = 3 6 12 24.
| Result | Value |
|---|---|
| Pattern | Geometric (r = 2) |
| Next terms | 48, 96, 192 |
Example 3
Inputs: Sequence = 1 2 4 7.
| Result | Value |
|---|---|
| Pattern | Not arithmetic or geometric |
The first line is the headline result (pattern). Below it the number Sequence Calculator lists next terms, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
How it decides
It checks whether the differences between consecutive terms are all equal, then whether the ratios are all equal. 2, 4, 8, 16 would be geometric with ratio 2.
Scope
Only arithmetic and geometric patterns are recognised. Fibonacci-type, quadratic and other patterns are not. At least 3 terms are needed, and more terms make the identification more reliable.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Sequence: entering "1, 2" shows "Enter at least 3 numbers." beside that field and no result.
Choosing between the Number Sequence Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Arithmetic Sequence Calculator](/math/arithmetic-sequence-calculator/) | first term, common difference and term number | a10 |
| [Geometric Sequence Calculator](/math/geometric-sequence-calculator/) | first term, common ratio and term number | a5 |
| [Slope Calculator](/math/slope-calculator/) | x₁, y₁ and x₂ | Slope |
| [LCM Calculator](/math/lcm-calculator/) | numbers | Least common multiple |
| [Factor Calculator](/math/factor-calculator/) | number | Factors |
Background: algebra
Many algebra calculators rest on the same ideas: write the problem in a standard form, identify the coefficients, apply the formula and check the answer by substituting it back. For a quadratic ax² + bx + c = 0 the roots are (−b ± √(b² − 4ac)) ÷ 2a, and the discriminant b² − 4ac decides the kind of roots: positive gives two real roots, zero gives one repeated root and negative gives two complex conjugate roots.
If a = 0 the equation is linear, not quadratic. A sign slip on the −b term shifts both roots by the same amount, so substitute your roots back to check.
Assumptions and limitations
- At least 3 terms
- Only arithmetic and geometric patterns
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for sequence to confirm this.
Frequently asked questions
What comes next in 1, 4, 9, 16?
25, a sequence of squares, which this tool does not detect.
What is the difference of 5, 8, 11?
The differences are 8 − 5 = 3 and 11 − 8 = 3, so the common difference is 3.
What is the ratio of 3, 6, 12?
Each term is twice the previous one (6 ÷ 3 = 2, 12 ÷ 6 = 2), so the common ratio is 2.
What does the Number Sequence Calculator calculate?
Identify an arithmetic or geometric sequence and find the next terms. It returns Pattern and Next terms.
What formula does the Number Sequence Calculator use?
arithmetic: constant difference; geometric: constant ratio. Checks differences then ratios (tolerance 1e-9); other sequences are reported as unrecognised.
What do I need to enter in the number Sequence Calculator?
You enter Sequence.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. At least 3 terms.
What are the limits of this calculator?
At least 3 terms. Only arithmetic and geometric patterns.
What is an example of a number Sequence result?
With sequence 2, 4, 6, 8, the pattern is Arithmetic (d = 2).
Related calculators
- Arithmetic Sequence Calculator — nth term and sum of an arithmetic sequence.
- Geometric Sequence Calculator — nth term and sum of a geometric sequence.
- Slope Calculator — Slope, angle, distance and line equation through two points.
- LCM Calculator — Least common multiple of two or more numbers.
- Factor Calculator — List every factor of a positive whole number.
- Quadratic Formula Calculator — Solve ax² + bx + c = 0, including complex roots.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.