What is Sequence Calculator?
Sequence Calculator helps you explore terms and sums in arithmetic or geometric sequences.
The main result is nth term, with a breakdown of sum of first n terms. The formula, example and assumptions below explain how to interpret it.
How to use Sequence Calculator
Use the example to get familiar with the form, then enter your own figures. Any rates in the example are illustrative. Check the field labels and units before calculating.
- Gather sequence, first term, common difference / ratio and term number. Use values from the same situation or reporting period.
- Replace the example sequence with your own value, then complete the other fields. Check the displayed units and each selected option.
- Select Calculate and read nth term with its result breakdown. Change one input and calculate again to compare a second scenario. Reset restores the original example.
- Choose sequence from Arithmetic and Geometric.
- Enter first term, at least -1000000000. Decimals are accepted.
- Enter common difference / ratio, at least -1000 and at most 1000. Decimals are accepted.
- Enter term number, at least 1 and at most 500. Use a whole number.
Sequence Calculator: a worked example
With the inputs below, the result is 29 (nth term). Follow the example, then replace these illustrative values with your own.
| Input or output | Example value |
|---|---|
| Sequence | Arithmetic |
| First term | 2 |
| Common difference / ratio | 3 |
| Term number | 10 |
| Nth term | 29 |
| Sum of first n terms | 155 |
Understanding the Sequence result
Read nth term alongside sum of first n terms. These describe different parts of the same calculation.
Displayed results use a readable number of decimal places. When checking a result by hand, keep extra precision until the last step. To compare scenarios, change one input at a time and keep the others fixed.
- Example Sum of first n terms: 155
Sequence Calculator: assumptions and common mistakes
A useful estimate starts with the right inputs. Check the following assumptions and limits before applying the result to your situation.
- Check the base value, sample definition and chosen operation. Display rounding should come after the calculation.
For wider guidance, visit NIST statistical handbook. The formula and scope of this specific tool are stated on this page.
