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Arithmetic sequence calculator
Find a term and partial sum of an arithmetic sequence.
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Nth term21
Sum of first n terms120
Calculator controls
How to calculate
Find a term and partial sum of an arithmetic sequence.
Nth term = a+(n-1)*d; Sum of first n terms = n*(2*a+(n-1)*d)/2
Worked example
Example inputs
First term: 3 · Common difference: 2 · Number of terms: 10
Example resultNth term: 21 · Sum of first n terms: 120
Assumptions and limits
Yes. A negative difference produces a decreasing sequence. A zero difference produces a constant sequence.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Each term changes by the same fixed difference. The sum is the number of terms multiplied by the average of the first and last terms.
When this tool is useful
Use this calculator when each term changes by the same fixed amount. It can find a later term without listing every value and total a fixed number of terms. For 3, 5, 7, …, the 10th term is 21 and the sum of the first 10 terms is 120.
Understanding your inputs
| Input | What to enter |
|---|---|
| First term | Enter a number of at least -1000000000 and no more than 1000000000. |
| Common difference | Enter a number of at least -1000000000 and no more than 1000000000. |
| Number of terms | Enter a number of at least 1 and no more than 1000000. |
Frequently asked questions
Can the common difference be negative?
Yes. A negative difference produces a decreasing sequence. A zero difference produces a constant sequence.
Go deeper: Read the worked Knowledge Base guide.