Calculating your sum of the series is straightforward once you know the Arithmetic Series Sum formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Arithmetic Series Sum Calculator.
What is Arithmetic Series Sum?
The Arithmetic Series Sum calculation tells you your sum of the series from a few simple inputs. The figure you are solving for here is the sum of the series.
The Arithmetic Series Sum formula
The core formula is:
Sum of the series = Number of terms (n) ÷ 2 × (2 × First term (a) + (Number of terms (n) - 1) × Common difference (d))Here is what each input means:
- First term (a) — a number. Example: 2.
- Common difference (d) — a number. Example: 3.
- Number of terms (n) — a number. Example: 5.
How to calculate it step by step
- Write down the first term (a) (for example, 2).
- Write down the common difference (d) (for example, 3).
- Write down the number of terms (n) (for example, 5).
- Apply the formula above to get your sum of the series.
- Double-check the result with the Arithmetic Series Sum Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| First term (a) | 2 |
| Common difference (d) | 3 |
| Number of terms (n) | 5 |
| Sum of the series | 40.0000 |
| Last term | 14.0000 |
With first term (a) of 2, common difference (d) of 3 and number of terms (n) of 5, the sum of the series works out to 40.0000.
Example 2
With first term (a) of 4, common difference (d) of 3 and number of terms (n) of 5, the sum of the series works out to 50.0000.
| Result | Value |
|---|---|
| Sum of the series | 50.0000 |
| Last term | 16.0000 |
Example 3
With first term (a) of 1, common difference (d) of 3 and number of terms (n) of 5, the sum of the series works out to 35.0000.
| Result | Value |
|---|---|
| Sum of the series | 35.0000 |
| Last term | 13.0000 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Arithmetic Series Sum Calculator does it instantly, for free, with the formula and a worked example built in.
Related calculators
Continue exploring math calculators with these tools: Margin of Error Calculator, Sample Size Calculator, Confidence Interval Calculator, Coefficient of Variation Calculator, Regular Heptagon Area Calculator.