Arithmetic Sequence Nth Term Calculator
Find the nth term of an arithmetic sequence from the first term, common difference, and term number. The calculator also shows the substitution and a short sequence check.
How the nth term is calculated: the calculator starts from the first term, counts the steps from term 1 to term n, and multiplies that count by the common difference. For large n, this is more useful than listing the whole sequence manually.
Arithmetic sequence nth term formula
Use this calculator when you know the first term, the common difference, and the term number n. It is focused on one output: the value of the nth term.
a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.
| Symbol | Meaning |
|---|---|
| a1 | first term of the arithmetic sequence |
| d | common difference between consecutive terms |
| n | term number, counted from 1 |
| an | nth term value |
| sum of the first n terms; this is a separate calculator |
- Enter the first term a1.
- Enter the common difference d; it may be negative or zero.
- Enter the target term number n.
- Read the nth term value and the numeric substitution.
Why the formula uses n minus 1
The first term is already in position 1, so moving from term 1 to term n takes one fewer step than the term number. When n equals 1, there are no steps and the answer is the first term.
Examples
| Case | a1 | d | n | an |
|---|---|---|---|---|
| Positive difference | 2 | 3 | 10 | 29 |
| Negative difference | 5 | -2 | 8 | -9 |
| Decimal difference | 1 | 0.5 | 20 | 10.5 |
| Zero difference | 7 | 0 | 100 | 7 |
Calculator limits
- n must be a positive integer.
- The form accepts term numbers up to 1,000,000,000.
- Decimal and very large values use JavaScript number precision.
- Use the arithmetic series sum calculator when the task asks for.
- If the first term or common difference is unknown, solve that parameter first.
Frequently Asked Questions
Sources and References
Calculations are based on the listed reference sources. Links open in a new tab.
Related Tools
Calculate an arithmetic sequence from the first term and common difference, or from the first two terms. See the nth term, the sum of the first terms, and the generated sequence.
Calculate the sum of the first n terms of an arithmetic series from the first term and common difference, or from the first and last terms.
Calculate a geometric sequence from the first term and common ratio, or from the first two terms. See the nth term, first n-term sum, and infinite sum when it converges.