Description
Rebase a geometric-sequence term to a supplied index.
Sequence calculations depend on the reference index, common difference or ratio, and whether a domain uses exact integers or real-valued arithmetic. Alternation depends on index parity; modular arithmetic chooses a representative in a fixed residue interval. A supplied local rule is not discovered from data and need not establish a complete recurrence or prediction model.
Rebase a geometric-sequence term to a supplied index.
When to use this tool
Use Geometric Sequence Reference Index Shift when you already have referenceTerm, commonRatio, referenceIndex, targetIndex and need to rebase a geometric-sequence term to a supplied index.
How to use the tool and how it works
- Enter referenceTerm, commonRatio, referenceIndex, targetIndex. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read targetTerm. Use the output convention below.
Require signed safe whole indices; return referenceTerm*commonRatio^(targetIndex-referenceIndex), forming the difference with BigInt before numeric exponentiation. Reject zero ratio for a backward shift.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| referenceTerm | Reference Term | Required. Finite number. |
| commonRatio | May be signed or zero; zero is rejected only for backward index shifts. | Required. Finite number. |
| referenceIndex | Reference Index | Required. Safe integer. |
| targetIndex | Target Index | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| targetTerm | Target Term | Required. Finite number. |
{
"input": {
"referenceTerm": 3,
"commonRatio": 2,
"referenceIndex": 4,
"targetIndex": 6
},
"output": {
"targetTerm": 12
}
}Limitations and assumptions
- A zero ratio at equal indices uses 0^0=1. Large index differences and floating-point powers can lose precision; no sequence model is inferred.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete sequence definition and initial conditions for recurrence analysis. Choose exact integer or rational arithmetic when large indices or exact terms matter; local reference shifts and residue operations do not discover a generating rule.
References
Similar or alternative tools
- Arithmetic Sequence Reference Index Shift
Rebase an arithmetic-sequence term using a supplied common difference.
- Alternating Sequence Sign At Index
Find an alternating sequence's sign relative to a supplied reference index.