What types of sequences can it detect?

It detects arithmetic sequences (constant difference between terms) and geometric sequences (constant ratio). If the numbers match neither, it returns a result of type unknown rather than forcing a pattern.

How many numbers do I need to enter?

At least three. With only two values almost any pattern could fit, so the calculator needs three or more terms to confirm a consistent difference or ratio before predicting the next terms.

How many future terms does it predict?

For a recognized arithmetic or geometric sequence it returns the next three terms by repeatedly applying the common difference or ratio to the last value you entered.

Why was my sequence labeled unknown?

It did not have a constant difference or a constant ratio across all consecutive terms. Patterns like Fibonacci or quadratic sequences fall outside the arithmetic and geometric checks this calculator performs.

Number Sequence Calculator

Sequence (comma-separated, min 3 numbers)

Next 3 Terms12.0000, 14.0000, 16.0000

Typearithmetic

Common Difference2.0000

Give this calculator a list of numbers and it identifies the underlying pattern, then predicts the next terms. It recognizes arithmetic sequences, where each term differs by a constant, and geometric sequences, where each term is multiplied by a constant ratio. When the data fits neither pattern it reports the sequence as unknown rather than guessing.

Formula

arithmetic: a(n+1) = a(n) + d; geometric: a(n+1) = a(n) * r

d: Common difference between consecutive terms in an arithmetic sequence
r: Common ratio between consecutive terms in a geometric sequence
a(n): The nth term of the sequence

How it works

Enter at least three numbers in order. Fewer than three values does not give enough information to detect a pattern.
The calculator first checks for a constant difference between consecutive terms (arithmetic), then for a constant ratio (geometric), using a tiny tolerance to allow for rounding.
If a pattern is found it reports the type, the common difference or ratio, and the next three terms by extending the rule from the last value. If neither fits, it labels the sequence unknown with no predicted terms.

Worked examples

Identify and extend the sequence 2, 5, 8, 11.

Differences: 5-2 = 3, 8-5 = 3, 11-8 = 3, all equal, so it is arithmetic with d = 3.
Add the common difference to the last term: 11 + 3 = 14.
Continue: 14 + 3 = 17, then 17 + 3 = 20.

Arithmetic sequence, common difference 3; the next three terms are 14, 17, and 20.

Identify and extend the sequence 3, 6, 12, 24.

Ratios: 6/3 = 2, 12/6 = 2, 24/12 = 2, all equal, so it is geometric with r = 2.
Multiply the last term by the ratio: 24 x 2 = 48.
Continue: 48 x 2 = 96, then 96 x 2 = 192.

Geometric sequence, common ratio 2; the next three terms are 48, 96, and 192.

Frequently asked questions

What types of sequences can it detect?: It detects arithmetic sequences (constant difference between terms) and geometric sequences (constant ratio). If the numbers match neither, it returns a result of type unknown rather than forcing a pattern.
How many numbers do I need to enter?: At least three. With only two values almost any pattern could fit, so the calculator needs three or more terms to confirm a consistent difference or ratio before predicting the next terms.
How many future terms does it predict?: For a recognized arithmetic or geometric sequence it returns the next three terms by repeatedly applying the common difference or ratio to the last value you entered.
Why was my sequence labeled unknown?: It did not have a constant difference or a constant ratio across all consecutive terms. Patterns like Fibonacci or quadratic sequences fall outside the arithmetic and geometric checks this calculator performs.

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