How it works
The first term is nonnegative and common difference positive. The sum covers the first n terms; inverse term count selects the positive integer branch. This form solves for first term; enter the known quantities in Sum of terms, Term count, Positive common difference.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Sum of terms | 120 | Formula symbol: S. Enter a numeric value. Must be greater than zero. |
| Term count | 10 | Formula symbol: n. Enter a numeric value. Use a whole number. Must be greater than zero. Allowed range: 2–10,000. |
| Positive common difference | 2 | Formula symbol: d. Enter a numeric value. Must be greater than zero. |
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
- 120
- Term count
- 10
- Positive common difference
- 2
Complete example results
- First term
- 3
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?
All terms use one numeric scale and indexing starts at 1. This form supports increasing arithmetic sequences with at least two terms.
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