How it works
The sum covers the first n positive terms. Ratio is greater than 1; inverse n must correspond to a whole term count. This form solves for last term; enter the known quantities in Sum of terms, Common ratio, Term count.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Sum of terms | 242 | Formula symbol: S. Enter a numeric value. Must be greater than zero. |
| Common ratio | 3 | Formula symbol: q. Enter a numeric value. Must be greater than zero. |
| Term count | 5 | Formula symbol: n. Enter a numeric value. Use a whole number. Must be greater than zero. Allowed range: 2–10,000. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Sum of terms
- 242
- Common ratio
- 3
- Term count
- 5
Complete example results
- Last term
- 162
Reading the result
The result solves for last term from the entered quantities. Check the result unit and the formula conditions before using it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
When can I use the last term result?
This is not an infinite-series sum. The last term and the sum of all terms are different quantities and belong in different fields.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: openstax.org