Sum of an Arithmetic Series Calculator
🔁 Sequences & series. Use the Sum of an arithmetic series formula to find sum sₙ, number of terms n, first term a, common difference d: pick the value you want, type the others, and the answer updates as you go.
Pick the ○ next to the value you want to find, fill in the others, and it solves as you type.
What each letter means
| Quantity | Unit |
|---|---|
| Sum Sₙ | no unit |
| Number of terms n | no unit |
| First term a | no unit |
| Common difference d | no unit |
Worked example
Find the sum sₙ when Number of terms n = 10, First term a = 2, Common difference d = 3.
Using Sn = n/2(2a + (n - 1)d): Sum Sₙ = 155.
Frequently asked questions
What is the formula for Sum of an arithmetic series?
Sn = n/2(2a + (n - 1)d).
What do the letters stand for, and what units are used?
Sum Sₙ, Number of terms n, First term a, Common difference d.
How do you calculate sum sₙ?
Put the values into Sn = n/2(2a + (n - 1)d). For example, with Number of terms n = 10, First term a = 2, Common difference d = 3, sum sₙ = 155.
Can I solve for a different value?
Yes. In the calculator above, pick the circle next to any value (sum sₙ, number of terms n, first term a, common difference d) and fill in the others: it rearranges the formula for you.
