Description
Check whether a proposed geometric middle term satisfies the squared-term relation within an absolute tolerance.
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 whether a proposed geometric middle term satisfies the squared-term relation within an absolute tolerance.
When to use this tool
Use it for geometric progression one term insertion test when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter left, inserted, right, tolerance. Use the stated units and boundary conventions.
- Run the calculation. Correct any input error before interpreting a result.
- Read residual, compatible. Inspect any known, defined, inclusion, or boundary flags before interpreting numeric values.
Test whether a proposed middle geometric term satisfies inserted squared = left*right. Return that signed residual and compare its absolute value inclusively with a nonnegative tolerance; left and inserted must be nonzero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Finite number. |
| inserted | Inserted | Required. Finite number. |
| right | Right | Required. Finite number. |
| tolerance | Absolute tolerance in squared-term units. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | Residual | Required. Finite number. |
| compatible | Compatible | Required. Boolean. |
{
"input": {
"left": 2,
"inserted": 4,
"right": 8,
"tolerance": 0
},
"output": {
"residual": 0,
"compatible": true
}
}Limitations and assumptions
- Tolerance is in squared-term units and is absolute rather than relative. Only the supplied three terms are checked, and approximate compatibility does not establish a fitted progression.
- The field tables describe structural bounds; the mechanics also state cross-field requirements. Malformed input shapes, disallowed keys, and invalid domains cause input errors. Results must remain finite and within the declared output contract. A successful false flag or zero placeholder is distinct from an error.
- 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 geometric progression one term insertion test, 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
- Arithmetic Geometric Single Term Formula
Evaluate one zero-based term of a supplied arithmetic-geometric progression.
- Arithmetic Progression Modular Residue Step
Advance a numeric residue by a supplied difference under floating-point modulo arithmetic.