Arithmetic Series Sum Calculator
Calculate the sum of an arithmetic series from 1 to n, or a custom range with a given step.
Sum Val
5,050
Num Terms100
Average Val50.5000
Arithmetic Series Sum
Formula (Gauss's Method)
Sum = n/2 × (first + last)
where n is the number of terms.
Famous Example
Gauss reportedly summed 1 to 100 as a child: Sum = 100/2 × (1 + 100) = 50 × 101 = 5050.
General Formula
For a series from a to b with step d:
Example Calculation
Sum all integers from 1 to 100.
- 01Number of terms = 100
- 02Sum = 100/2 × (1 + 100)
- 03= 50 × 101
- 04= 5050
Frequently Asked Questions
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