How many terms do I need to enter?

At least 3 terms are required to identify an arithmetic or geometric sequence. Quadratic detection needs at least 4 terms because it relies on second differences.

What if my sequence is none of the three types?

The tool will report that no standard pattern was found. Only arithmetic (linear), geometric (exponential), and quadratic sequences are supported. Try adding more terms to confirm the pattern.

Can the common ratio be negative or fractional?

Yes. Geometric sequences with negative ratios alternate sign (e.g. 2, -4, 8, -16), and fractional ratios produce decreasing sequences (e.g. 16, 8, 4, 2). Both are handled correctly.

What is a quadratic sequence?

A quadratic sequence has a constant second difference — that is, the differences between consecutive differences are equal. The nth term takes the form an² + bn + c. Example: 1, 4, 9, 16, 25 (perfect squares).

Are floating-point sequences supported?

Yes. You can enter decimal values such as 1.5, 3.0, 4.5 and the tool will detect the pattern and compute terms with the same precision.

Sequence Nth Term Finder

Paste a list of numbers, get the nth term formula for arithmetic, geometric, or quadratic sequences, and evaluate any term.

Enter Sequence Terms

Terms (comma-separated, e.g. 2, 5, 8, 11)

Find term at position n

Quick examples

Enter a sequence and click Find

Summary

Enter a list of numbers separated by commas and this tool automatically identifies whether the sequence is arithmetic (constant difference), geometric (constant ratio), or quadratic (constant second difference). It then derives the nth term formula and lets you evaluate the sequence at any position n.

How it works

Enter at least 3 terms of your sequence, separated by commas.
The tool checks first differences to detect an arithmetic sequence.
If not arithmetic, it checks ratios to detect a geometric sequence.
If neither, it checks second differences to detect a quadratic sequence.
The matched formula is displayed with its coefficients filled in.
Enter any value of n to compute that specific term.

Use cases

Solve homework problems asking for the nth term rule.
Verify whether a data series follows a linear, exponential, or quadratic pattern.
Generate future values of a known sequence without listing every term.
Check exam answers for arithmetic and geometric progressions.
Explore pattern recognition in number puzzles.
Model sequences in physics, finance, or computer science exercises.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu