Arithmetic & Geometric Sequences
Local ProcessingCalculate the sum Sₙ = (n / 2) × (2a₁ + (n - 1) × d) of the first n terms of an arithmetic progression.
How It Works & Processing Standards
Enter values above to calculate results automatically. Check each input field for guidance and units.
Tool processing runs in your browser. If you create a calculator or conversion share link, its values are included in the URL. See the privacy policy for account, analytics and advertising data.
Choose arithmetic sum, arithmetic nth term, geometric nth term or geometric sum under "Calculation".
What You Can Do
- Arithmetic
- nth term a₁ + (n − 1)d; sum n(2a₁ + (n − 1)d) ÷ 2
- Geometric
- nth term a₁ × r^(n − 1); sum a₁(1 − rⁿ) ÷ (1 − r)
How to Use Arithmetic & Geometric Sequences
- 1Choose a calculationThe sequence type and whether you want a term or a sum.
- 2Enter valuesFirst term a₁, difference d or ratio r, and number of terms n.
- 3Read the resultCopy it.
Examples
Sum of 1 to 100
Input: a₁ 1, d 1, n 100 (arithmetic sum)
Result: 5,050
6th term of 3, 6, 12, …
Input: a₁ 3, r 2, n 6
Result: 96
Common Use Cases
- Checking sequence homework
- Total of savings that grow by a fixed amount each month
- The nth value of something that doubles
Frequently Asked Questions (FAQ)
What if the ratio is 1?
The geometric sum becomes a₁ × n, which the tool handles.
Can n be 0?
A sum with n = 0 is 0. For the nth term, n must be 1 or more.