Sum of Series Calculator
Arithmetic, geometric and infinite series sums in one place.
Enter your values
ⓘ Live results
Results
- Sum of n terms
- 366
- nth term
- 58
- Average term
- 30.5
- Common difference
- 5
- Series type
- Arithmetic
Quick answer
An arithmetic series sums to n/2 × (2a + (n−1)d), and a geometric series to a(1 − rⁿ) ÷ (1 − r), converging to a ÷ (1 − r) when |r| < 1.
Sₙ = n/2(2a + (n−1)d) or a(1 − rⁿ)/(1 − r)
How to use the Sum of Series Calculator
- 1Pick arithmetic or geometric.
- 2Enter the first term and the difference or ratio.
- 3Enter how many terms you want summed — the infinite sum appears automatically when it converges.
Worked example
Using the values the calculator loads with:
Inputs
- Series typeArithmetic (add d each time)
- First term a3
- Common difference d or ratio r5
- Number of terms n12
Results
- Sum of n terms366
- nth term58
- Average term30.5
- Common difference5
- Series typeArithmetic
Frequently asked questions
When does an infinite geometric series converge?
Only when the absolute value of the ratio is under 1; then the sum is a ÷ (1 − r).
What if the ratio is exactly 1?
Every term is the same, so the sum is simply a × n.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.