Why not just add up every number?

The formula gives the exact same result instantly for any range, even ranges with millions of terms, without looping through each number.

Does this work for negative numbers?

Yes, you can enter a negative start value and the formula still correctly sums the consecutive integer range.

Sum of Consecutive Integers Calculator

Calculate the sum of a consecutive range of integers using the arithmetic series formula, without adding every number one by one. Works for any start and end value, including the classic '1 to n' case.

Inputs

Results

Sum: 55
Number of Terms: 10

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Formula

Sum = n × (first + last) / 2, where n = number of terms

Learn How This Works

Number Theory and Sequences: Fibonacci, Combinations, and Basic Operations

The Fibonacci sequence, combinations with repetition, sums of consecutive integers, reciprocals, and absolute value — five foundational number theory calculations.

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