Description
Check one arithmetic-progression transition with a signed residual and exact difference comparison.
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 arithmetic-progression transition with a signed residual and exact difference comparison.
When to use this tool
Use it for sequence: arithmetic term adjacent residual when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter current, next, expectedDifference. 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 arithmetic transition using residual = next-current-expectedDifference and exact equality of next-current with expectedDifference. Return both fields inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| current | Current | Required. Finite number. |
| next | Next | Required. Finite number. |
| expectedDifference | Expected Difference | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
{
"input": {
"current": 2,
"next": 5,
"expectedDifference": 2
},
"output": {
"result": {
"residual": 1,
"exactlyConsistent": false
}
}
}Limitations and assumptions
- Equality uses the performed floating-point operations with no tolerance. This does not fit a trend, check other terms, or establish significance of a measured residual.
- 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: arithmetic 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: Geometric Term Adjacent Residual
Check one geometric-progression transition using an exact product comparison and a signed residual.
- Arithmetic Geometric Single Term Formula
Evaluate one zero-based term of a supplied arithmetic-geometric progression.