Arithmetic Series Sum Table: Sum of the series by First term (a)
Reference table of sum of the series for Arithmetic Series Sum across a range of first term (a) values — exact, engine-computed figures you can read off at a glance.
Arithmetic Series Sum Calculator
Verified formula Updated Jun 2026 Private — runs on your device
Verified formula
Private
Sum of the series
40.0000
- Last term
- 14.0000
For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.
How to use the Arithmetic Series Sum Calculator
The Arithmetic Series Sum Calculator works out your sum of the series, along with 1 related figure in an instant. Enter first term (a), common difference (d) and number of terms (n) and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.
- Enter the first term (a).
- Enter the common difference (d).
- Enter the number of terms (n).
- Read off your sum of the series, together with last term — the calculator updates automatically, with no button to press.
Formula
The Arithmetic Series Sum Calculator uses the formula:
Sum of the series = Number of terms (n) ÷ 2 × (2 × First term (a) + (Number of terms (n) - 1) × Common difference (d))
Worked example
For example, with first term (a) of 2, common difference (d) of 3 and number of terms (n) of 5, the sum of the series is 40.0000.
| First term (a) | 2 |
|---|---|
| Common difference (d) | 3 |
| Number of terms (n) | 5 |
| Sum of the series | 40.0000 |
|---|---|
| Last term | 14.0000 |
Results are estimates for educational use, not professional advice.
Frequently asked questions
It is the sum of an arithmetic sequence, where each term differs by a fixed amount. 2 + 5 + 8 + 11 + 14 sums to 40.
Sum = n ÷ 2 × (2a + (n − 1)d), using the first term a, common difference d and number of terms n.
The last term is a + (n − 1)d, the first term plus the difference applied n − 1 times.
Yes. A negative difference gives a decreasing series, and the formula still applies.
Enter the first term (a). Enter the common difference (d). Enter the number of terms (n). Read off your sum of the series, together with last term — the calculator updates automatically, with no button to press.
Related guides
How to Calculate Arithmetic Series Sum: Formula, Steps & Examples
Learn how to calculate Arithmetic Series Sum — the formula explained step by step, with worked examples and a free calculator to check your answer.