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Series Calculator
About the Series Calculator
Find the sum of an arithmetic or geometric series from the first term, the common difference or ratio, and the number of terms.
How to use the Series Calculator
- Enter the first term a₁, the common difference d and the number of terms n.
- Use Add Series Field for more series and read the sum.
Formula and method
Arithmetic series: Sₙ = n ÷ 2 × (2a₁ + (n − 1)d). Geometric series: Sₙ = a₁ × (1 − rⁿ) ÷ (1 − r).
Worked example
The sum of the numbers 1 to 100 (a₁ = 1, d = 1, n = 100) is 5,050. The geometric series 1 + 2 + 4 + ... with 10 terms adds up to 1,023.
Tips
- A geometric series converges to a₁ ÷ (1 − r) if |r| is less than 1.
Frequently Asked Questions
A sequence is a list of numbers. A series is the sum of the terms of a sequence.