Math
July 13, 2026 · 8 Min Read
Consecutive Integers Calculator – Guide & Formulas
Find consecutive integers that sum to a target value. Solve for unknown integers in sequences and verify results with step-by-step algebra.
Try the free calculator
Put these formulas into practice with our instant, step-by-step Consecutive Integers Calculator.
Find consecutive integers that add up to any target sum. Enter how many consecutive integers you need and the target sum to solve for the sequence with algebraic steps.
Key Takeaway
Use the free Consecutive Integers Calculator to find consecutive integers that sum to a target value. solve for unknown integers in sequences and verify results with step-by-step algebra. Get instant results with step-by-step explanations.
How to Use the Consecutive Integers Calculator
- Enter the number of consecutive integers in the sequence (e.g., 3 for three consecutive integers).
- Enter the target sum you want the integers to add up to.
- Review the solution showing the starting integer and the full sequence.
- Follow the verification step showing the sum of the integers equals your target.
The Formula
Sum of n consecutive integers starting from x: S = n·x + n(n-1)/2. Solving for x: x = (S - n(n-1)/2) / n.
Variable Definitions
- S: The target sum of the consecutive integers
- n: The number of consecutive integers in the sequence
- x: The first (smallest) integer in the sequence
Three Consecutive Integers That Sum to 72
Find three consecutive integers whose sum is 72.
- Step 1: Set up the equation. For 3 consecutive integers starting at x: x + (x+1) + (x+2) = 72.
- Step 2: Simplify: 3x + 3 = 72.
- Step 3: Solve for x: 3x = 69, so x = 23.
- Step 4: The three consecutive integers are 23, 24, and 25.
- Step 5: Verify: 23 + 24 + 25 = 72 —