Enter a target sum, choose how many consecutive integers you want (2, 3, 4, or 5), and select whether you want regular, odd, or even consecutive integers — the Consecutive Integers Calculator finds the starting integer and lists all values whose sum matches your target. You also get the full equation breakdown and a visual chart of each integer's contribution.
First (Starting) Integer
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Verified Sum
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Consecutive Integers Found
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Equation
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Consecutive integers are whole numbers that follow each other in order with a difference of 1 between each pair. For example, 4, 5, 6 and −2, −1, 0, 1 are sets of consecutive integers. They include positive numbers, negative numbers, and zero.
For n consecutive integers starting at x, the sum equals n·x + (0+1+2+…+(n−1)) = S. Solving for x gives x = (S − n(n−1)/2) / n. If x is a whole integer, a valid solution exists. This calculator handles that algebra for you automatically.
Let the integers be n, n+1, and n+2. Their sum is 3n + 3 = S, so n = (S − 3) / 3. For example, if the sum is 45: n = (45 − 3) / 3 = 14, giving integers 14, 15, 16.
Consecutive odd integers differ by 2 (e.g., 1, 3, 5, 7) and consecutive even integers also differ by 2 (e.g., 2, 4, 6, 8). Both are represented as n, n+2, n+4, … The formulas differ from regular consecutive integers because the step is 2 instead of 1.
Let the integers be n and n+1. Their sum is 2n + 1 = S, so n = (S − 1) / 2. This works only when S is odd. If S is even, there are no two consecutive integers with that sum (though two consecutive even or odd integers may work).
Not always. A valid solution requires the starting integer to be a whole number (integer). If the calculation produces a decimal or fraction, no set of consecutive integers of that type and count sums to the target. The calculator will indicate this in such cases.
Yes. Consecutive integers extend infinitely in both directions. For example, the three consecutive integers that sum to −6 are −3, −2, and −1. The calculator handles negative starting values correctly.
The sum of all integers from a to b inclusive is (b − a + 1) × (a + b) / 2. For example, the sum from 1 to 100 is 100 × 101 / 2 = 5050. This is related to the triangular number formula n(n+1)/2.