How it works
Each term multiplies the previous by q. Positive first term and q>1 select the increasing branch; the inverse index must be an integer. This form solves for first term; enter the known quantities in Last term, Common ratio, Term index.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Last term | 162 | Formula symbol: u. 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 index | 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.
- Last term
- 162
- Common ratio
- 3
- Term index
- 5
Complete example results
- First term
- 2
Reading the result
The result solves for first 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 first term result?
The first term has index 1 and this form uses index 2 or later. Negative ratios, constant sequences and alternating branches are outside this model.
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