Sum of a Geometric Series Calculator
🔁 Sequences & series. Use the Sum of a geometric series formula to find sum sₙ, first term a, common ratio r, number of terms n: 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 |
| First term a | no unit |
| Common ratio r | no unit |
| Number of terms n | no unit |
Worked example
Find the sum sₙ when First term a = 3, Common ratio r = 2, Number of terms n = 10.
Using Sn = (a(1 - rⁿ))/(1 - r): Sum Sₙ = 3069.
Frequently asked questions
What is the formula for Sum of a geometric series?
Sn = (a(1 - rⁿ))/(1 - r).
What do the letters stand for, and what units are used?
Sum Sₙ, First term a, Common ratio r, Number of terms n.
How do you calculate sum sₙ?
Put the values into Sn = (a(1 - rⁿ))/(1 - r). For example, with First term a = 3, Common ratio r = 2, Number of terms n = 10, sum sₙ = 3069.
Can I solve for a different value?
Yes. In the calculator above, pick the circle next to any value (sum sₙ, first term a, common ratio r, number of terms n) and fill in the others: it rearranges the formula for you.
