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:

  • Number of terms: floor((b - a) / d) + 1
  • Sum = n/2 × (first + last)
  • Example Calculation

    Sum all integers from 1 to 100.

    1. 01Number of terms = 100
    2. 02Sum = 100/2 × (1 + 100)
    3. 03= 50 × 101
    4. 04= 5050

    Frequently Asked Questions

    Learn More

    How to Calculate Percentages - Complete Guide

    Learn how to calculate percentages step by step. Covers finding a percentage of a number, percentage change, reverse percentages, and real-world applications.

    Related Calculators