Last updated October 13, 2026 · Report an error
An arithmetic series is the sum of a sequence where each term increases (or decreases) by the same fixed amount — adding up all those terms one by one gets tedious fast as the sequence grows longer.
This calculator finds the sum of an arithmetic series directly from its first term, common difference, and number of terms, with a full step-by-step solution.
How it works
Enter the first term, the common difference between consecutive terms, and the number of terms in the series. The calculator finds the last (nth) term, then applies the arithmetic series sum formula to find the total.
- Enter first term (a).
- Enter common difference (d).
- Enter number of terms (n).
- Click Calculate to see your results.
Examples
The sum of the first 10 terms starting at 3, increasing by 5
With a first term of 3, a common difference of 5, and 10 terms, the last term is 48 and the sum of the series is 255.
Who should use it
- Finding the total of a sequence of evenly-spaced payments, deposits, or measurements.
- Solving arithmetic series problems for coursework or exam preparation.
Industry applications
- Mathematics education
- Financial modeling involving evenly-stepped payment schedules
Advantages
- Calculates both the sum and the last term in one step.
- Includes a complete, formula-based step-by-step solution.
Limitations
- Only applies to arithmetic (constant-difference) series, not geometric or other sequences.
Common mistakes to avoid
- Confusing the common difference (the gap between terms) with the number of terms (how many terms are in the series).
- Expecting the "last term" and "sum" to be the same thing — the last term is one value in the series, while the sum totals every term.
Best practices
- Double-check whether you have the common difference or the last term given — if you have the last term instead, you can back-calculate the common difference first.
Tips
- If you only know the first and last term (not the common difference), you can still find the sum using \(S_n = \frac{n}{2}(a+a_n)\) directly, without needing the common difference at all.