ClarityHow to use this tool
- Enter first term, common ratio, number of terms.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
Input reference and sample values
Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.
| Input | Format and units | Sample |
|---|---|---|
| First term | Numeric value. | 2 |
| Common ratio | Numeric value. Minimum: -1000000. Maximum: 1000000. | 3 |
| Number of terms | Numeric value. Minimum: 1. Maximum: 1000. | 5 |
Result for these sample inputs
162
- Term number
- 5
- Sum of requested terms
- 242
- First 5 terms
- 2, 6, 18, 54, 162
Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.
The method, explained
Term n = first term × ratio raised to (n − 1). The tool multiplies successively and adds the requested terms, including the ratio = 1 case without division by zero.
For first term 2 and ratio 3, five terms are 2, 6, 18, 54, 162. Their sum is 242.
What to keep in mind
Calculates a finite sequence, not an infinite sum. Up to 1,000 terms; only the first 20 are listed. Values beyond 10^100 are rejected, and extremely small values may underflow in browser arithmetic.
Common questions
What does a negative ratio do?
For a nonzero first term, signs alternate. For example, ratio −2 produces 1, −2, 4, −8.
What happens with a zero ratio?
The first term stays as entered; every later term is zero.
Methodology maintained by ClarityKit. How these tools are built and checked.