Arithmetic Sequence Calculator
Find the nth term and the sum of an arithmetic sequence from the first term and common difference.
Your inputs
Results
Term 10 (aₙ)
39
- Sum of the first 10 terms
- 210
- First 10 terms
- 3, 7, 11, 15, 19, 23, 27, 31, 35, 39
✓Exact calculation — rounded only for display
What this calculator does
An arithmetic sequence adds the same difference each step, like 3, 7, 11, 15.
Formula and method
aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ) ÷ 2
Worked example
Calculated by this tool with its default inputs:
Inputs
- First term (a₁): 3
- Common difference (d): 4
- Number of terms (n): 10
Results
- Term 10 (aₙ): 39
- Sum of the first 10 terms: 210
- First 10 terms: 3, 7, 11, 15, 19, 23, 27, 31, 35, 39
How to read the results
The sum formula pairs first and last terms, as Gauss is said to have done.
Assumptions and limitations
- The first 20 terms are listed.
Questions
What if d is negative?
The sequence decreases; the formulas still apply.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 3 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy