Description
Check one geometric-progression transition using an exact product comparison and a signed residual.
A sequence rule specifies how terms relate. Checking one transition, advancing a recurrence, and bounding an infinite tail answer different questions. A calculation from supplied coefficients assumes that rule; it does not infer it from observations.
Check one geometric-progression transition using an exact product comparison and a signed residual.
When to use this tool
Use it for sequence: geometric term adjacent residual when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter current, next, expectedRatio. Use the stated units and boundary conventions.
- Run the calculation. Correct any input error before interpreting a result.
- Read result. Inspect any known, defined, inclusion, or boundary flags before interpreting numeric values.
Check one geometric transition using residual = next - current*expectedRatio and an exact comparison of next with that product. Results are nested inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| current | Current | Required. Finite number. |
| next | Next | Required. Finite number. |
| expectedRatio | Expected Ratio | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
{
"input": {
"current": 2,
"next": 7,
"expectedRatio": 3
},
"output": {
"result": {
"residual": 1,
"exactlyConsistent": false
}
}
}Limitations and assumptions
- Zero current is supported because no division occurs. Exactly consistent means binary64 equality, not agreement within a measurement tolerance or evidence that an entire sequence is geometric.
- The result object is nested under result. Malformed input or arithmetic outside the supported range produces an error rather than a successful comparison.
- Numeric arithmetic uses binary floating point. Exact comparisons have no hidden tolerance or decimal rounding; negative zero is exported as zero. Decimal-text integer operations retain the exactness specifically stated above.
Alternative or Complementary methods
For sequence: geometric term adjacent residual, check the source records and the supplied rule before comparing the result with another method. Use exact integer or symbolic arithmetic when a numerical equality is insufficient.
References
Similar or alternative tools
- Sequence: Arithmetic Term Adjacent Residual
Check one arithmetic-progression transition with a signed residual and exact difference comparison.
- Arithmetic Geometric Single Term Formula
Evaluate one zero-based term of a supplied arithmetic-geometric progression.