Description
Evaluate one zero-based term of a supplied arithmetic-geometric progression.
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.
Evaluate one zero-based term of a supplied arithmetic-geometric progression.
When to use this tool
Use it for arithmetic geometric single term formula when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter initial, difference, ratio, index. Use the stated units and boundary conventions.
- Run the calculation. Correct any input error before interpreting a result.
- Read term. Inspect any known, defined, inclusion, or boundary flags before interpreting numeric values.
Evaluate term = (initial + index*difference)*ratio^index for a zero-based integer index from zero through 1000.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| initial | Initial | Required. Finite number. |
| difference | Difference | Required. Finite number. |
| ratio | Dimensionless ratio of compatible quantities under the stated formula. | Required. Finite number. |
| index | Zero-based selected index, unless a different convention is stated in the mechanics. | Required. Safe integer; minimum 0; maximum 1000. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| term | Term | Required. Finite number. |
{
"input": {
"initial": 2,
"difference": 3,
"ratio": 2,
"index": 3
},
"output": {
"term": 88
}
}Limitations and assumptions
- The caller supplies the arithmetic-geometric model. At index zero the power factor is one, including ratio zero; large powers or products can fail finite-output validation.
- 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 arithmetic geometric single term formula, 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
- Geometric Series Single Tail Bound
Calculate an absolute tail bound from a first omitted magnitude and a supplied geometric domination ratio.
- Arithmetic Progression Modular Residue Step
Advance a numeric residue by a supplied difference under floating-point modulo arithmetic.