Math Tools
Number Sequence Calculator
Enter a number sequence, detect common patterns, and predict the next terms for arithmetic, geometric, Fibonacci-like, and recursive sequences.
Sequence Predictor
Enter a number sequence and extend it when a recognizable pattern is detected.
Example: 2, 4, 6, 8 or 3 9 27
Result
Detected type
arithmetic
Rule
Arithmetic sequence with common difference 2.
Extended sequence
2, 4, 6, 8, 10, 12, 14
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Supported sequence types
This calculator detects arithmetic, geometric, and Fibonacci-like sequences, then predicts the next values based on the detected rule.
What is a number sequence calculator?
A number sequence calculator is a math tool that helps identify the pattern in a sequence of numbers and predict the next terms. Instead of solving the pattern manually, you can enter the sequence and let the calculator detect whether it follows an arithmetic, geometric, Fibonacci-like, or related rule.
This is useful for students, teachers, exam preparation, homework, and anyone working with sequence patterns in algebra or number theory. It gives a quick result and also shows the detected rule so the sequence makes more sense.
Common sequence types explained
Arithmetic sequence
An arithmetic sequence adds or subtracts the same number each time. Example: 2, 4, 6, 8.
Geometric sequence
A geometric sequence multiplies or divides by the same number each time. Example: 3, 9, 27, 81.
Fibonacci-like sequence
Each term is formed by adding the previous two terms. Example: 1, 1, 2, 3, 5, 8.
Recursive sequence
A recursive sequence defines each new term using one or more earlier terms according to a rule.
Sequence type comparison table
| Sequence type | Pattern | Example | Common use |
|---|---|---|---|
| Arithmetic sequence | Add or subtract the same value | 4, 7, 10, 13 | Linear patterns, equal steps, simple term rules |
| Geometric sequence | Multiply or divide by the same value | 2, 6, 18, 54 | Growth, decay, ratios, exponential-style patterns |
| Fibonacci-like sequence | Add the previous two terms | 1, 1, 2, 3, 5, 8 | Recursive patterns and classic sequence problems |
| Recursive sequence | Use earlier terms to generate later terms | 2, 5, 11, 23 | Rules based on previous outputs |
Number sequence examples and predicted next terms
These examples show how common number sequence patterns are identified and extended.
| Sequence type | Input sequence | Rule | Next terms |
|---|---|---|---|
| Arithmetic sequence | 2, 4, 6, 8 | Add 2 each time | 10, 12, 14 |
| Geometric sequence | 3, 9, 27 | Multiply by 3 each time | 81, 243, 729 |
| Fibonacci-like sequence | 1, 1, 2, 3, 5 | Add the previous two terms | 8, 13, 21 |
| Decreasing arithmetic sequence | 20, 15, 10, 5 | Subtract 5 each time | 0, -5, -10 |
How to find the pattern in a number sequence
To find a pattern in a number sequence, first check whether the difference between terms stays the same. If it does, the sequence is arithmetic. If the ratio between terms stays the same, the sequence is geometric.
If neither pattern fits, look at whether each term is formed from previous terms, such as in Fibonacci-like or recursive sequences. Entering more terms into a sequence calculator often makes the pattern easier to detect.
When to use a sequence predictor
A sequence predictor is useful when you need to find the next number in a pattern, verify a homework answer, check a sequence rule, or understand how a pattern grows over time.
It is especially helpful for arithmetic sequence questions, geometric sequence problems, Fibonacci number patterns, exam practice, and classroom exercises where speed and accuracy matter.
Sequence calculator FAQ and common number sequence questions
What is a number sequence calculator?
A number sequence calculator identifies the pattern in a list of numbers and predicts the next terms when a recognizable rule is found.
How do you find the next term in an arithmetic sequence?
Find the constant difference between terms and add it to the last term. For example, in 2, 4, 6, 8, the next term is 10.
How do you find the next term in a geometric sequence?
Find the constant ratio between terms and multiply the last term by that ratio. For example, in 3, 9, 27, the next term is 81.
Can this number sequence calculator detect Fibonacci patterns?
Yes. It can recognize Fibonacci-like sequences where each term is the sum of the previous two terms, such as 1, 1, 2, 3, 5.
Why is my sequence not being detected correctly?
Some sequences are more complex and may need more terms before a clear pattern can be found. Try entering additional values to help the calculator identify the rule.
Choose a sequence calculator
Explore calculators for arithmetic, geometric, Fibonacci, quadratic, recursive, and sequence sum problems.
Arithmetic Sequence Calculator
Find the nth term, common difference, and sum of an arithmetic sequence.
Geometric Sequence Calculator
Find the nth term, common ratio, and sum of a geometric sequence.
Fibonacci Calculator
Generate Fibonacci terms and find the nth Fibonacci number.
Quadratic Sequence Calculator
Work with sequences that have a constant second difference.
Sequence Predictor
Enter a sequence and predict the next term when a pattern is detected.
Recursive Sequence Calculator
Generate terms from a recursive rule and starting value.
Sequence Sum Calculator
Calculate the sum of arithmetic, geometric, and other sequence types.