What this calculator does
The Next Number in Sequence Calculator looks at a list of numbers you enter and figures out the pattern, then predicts the upcoming terms. It automatically tests whether your sequence is arithmetic (each term changes by a fixed amount) or geometric (each term is multiplied by a fixed factor), and uses the right rule to continue the pattern.
How to use it
Type your sequence into the box separated by commas, for example 3, 6, 9, 12. Choose how many future terms you want predicted, then submit. The calculator reports the detected sequence type, the common difference (d) or common ratio (r), and the list of next terms.
The formula explained
For an arithmetic sequence the difference between consecutive terms is constant: \(d = a_2 - a_1\). Each new term is the previous term plus \(d\), so $$a_{n+1} = a_n + d.$$ For a geometric sequence the ratio between consecutive terms is constant: \(r = a_2 \div a_1\). Each new term is the previous term times \(r\), so $$a_{n+1} = a_n \cdot r.$$ The tool checks every consecutive pair, so it only reports a pattern when it holds across the whole list.
Worked example
Given 2, 4, 8, 16: the differences (2, 4, 8) are not constant, so it is not arithmetic. The ratios (\(4 \div 2 = 2\), \(8 \div 4 = 2\), \(16 \div 8 = 2\)) are all 2, so it is geometric with \(r = 2\). The next three terms are $$16 \cdot 2 = 32, \quad 32 \cdot 2 = 64, \quad 64 \cdot 2 = 128.$$
FAQ
What if my sequence is neither type? If the differences and ratios are both inconsistent, the calculator reports that it is not a simple arithmetic or geometric sequence.
Can it handle decimals and negatives? Yes. Negative steps (like 10, 7, 4) and fractional ratios (like 8, 4, 2) are fully supported.
How many terms do I need? At least two numbers are required to detect a pattern; more terms give a more reliable result.
