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Math / Number Sequence

Number Sequence Calculator

Inspect an ordered list for a constant arithmetic difference or constant geometric ratio, then extend the sequence by one term. It also reports the observed step pattern so a simple sequence can be checked without guessing its rule. For an arithmetic sequence, the next term is last + d where d is the repeated difference. For a geometric sequence, it is last × r where r is the repeated ratio.

Your inputs

Make it your own
Calculator settings

Your result
15
Next arithmetic term
Common difference
4

Example inputs shown. Adjust them to explore.

A familiar situation

Extend a simple arithmetic or geometric number pattern when checking a worksheet.

How to use this calculator

  1. Enter sequence terms.
  2. Select Calculate to see the answer and its breakdown.
  3. Keep a scenario, change an input and compare the results.

Use consistent units and check the assumptions below before applying the result.

How number sequence is calculated

For an arithmetic sequence, the next term is last + d where d is the repeated difference. For a geometric sequence, it is last × r where r is the repeated ratio. The sequence 3, 7, 11 has a repeated difference of 4, so its next term is 15.

Arithmetic next term = last+d; geometric next term = last×r.
A worked example

The sequence 3, 7, 11 has a repeated difference of 4, so its next term is 15.

Assumptions & useful context

The result depends on the values you enter and the method described above. Displayed numbers may be rounded; calculations use the unrounded values. Check that this model matches your situation before relying on it.

Frequently asked questions

Can every sequence be uniquely continued?

No. Many rules can fit the same finite list; this tool tests only arithmetic and geometric patterns.

What if the differences and ratios are both inconsistent?

The calculator reports that neither supported pattern fits.

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