Arithmetic Series Sum Calculator
Sum of the first n terms of an arithmetic sequence.
Enter your values
Enter the first term a1 you are working with.
Enter the common difference d you are working with.
Enter the number of terms n you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Sum of series
- 255
- Last term (a_n)
- 48
- Number of terms
- 10
Quick answer
The sum of an arithmetic series is n/2 times the sum of the first and last terms.
S_n = n/2 * (2a + (n-1)d)
At a glance
| What it does | Sum of the first n terms of an arithmetic sequence. |
|---|---|
| Category | Math |
| Inputs needed | First term a1, Common difference d, Number of terms n |
| Main output | Sum of series |
| Formula | S_n = n/2 * (2a + (n-1)d) |
| Cost | Free — no sign-up, no download |
How to use the Arithmetic Series Sum Calculator
- 1Enter the first term and the common difference between terms.
- 2Enter how many terms to sum.
- 3The formula multiplies the average of the first and last term by the count.
Inputs explained
- First term a1
- Enter the first term a1 you are working with.
- Common difference d
- Enter the common difference d you are working with.
- Number of terms n
- Enter the number of terms n you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- First term a13
- Common difference d5
- Number of terms n10
Results
- Sum of series255
- Last term (a_n)48
- Number of terms10
Frequently asked questions
What if d is negative?
The sequence decreases, and the formula still works unchanged.
How do I find just the nth term?
Use a + (n-1)d without the summation.
What do I need to enter into the Arithmetic Series Sum Calculator?
Just 3 values: first term a1, common difference d, number of terms n. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Arithmetic Series Sum Calculator work out the answer?
The sum of an arithmetic series is n/2 times the sum of the first and last terms. It applies the formula S_n = n/2 * (2a + (n-1)d) and shows the working so you can check each step by hand.
Is the Arithmetic Series Sum Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.