🔢 Consecutive Integers Calculator
Find consecutive integers that add up to a given sum
Default: 3 numbers
How to Use This Calculator
Enter the Target Sum
Input the total sum you want the consecutive integers to add up to.
Specify Count
Enter how many consecutive integers you need (default is 3).
View Solution
See the consecutive integers that sum to your target, or no solution if impossible.
Formula
For n consecutive integers starting at x:
Sum = nx + n(n-1)/2
First integer x = (Sum - n(n-1)/2) / n
Example 1: Find 3 consecutive integers that sum to 24
Sum = 24, n = 3
x = (24 - 3×2/2) / 3 = (24 - 3) / 3 = 7
Answer: 7, 8, 9 (7+8+9=24)
Example 2: Find 4 consecutive integers that sum to 34
Sum = 34, n = 4
x = (34 - 4×3/2) / 4 = (34 - 6) / 4 = 7
Answer: 7, 8, 9, 10 (7+8+9+10=34)
About Consecutive Integers Calculator
The Consecutive Integers Calculator finds a set of consecutive integers (numbers in sequence like 5, 6, 7) that add up to a specified sum. This is useful for solving word problems, puzzles, and algebraic equations.
When to Use This Calculator
- Math Problems: Solve consecutive integer word problems
- Algebra: Find consecutive integers for equations
- Puzzles: Solve number sequence puzzles
- Verification: Check if a problem has a solution
- Educational Use: Learn consecutive integer patterns
Why Use Our Calculator?
- ✅ Instant Solution: Find consecutive integers immediately
- ✅ Flexible Count: Any number of consecutive integers
- ✅ Verification: Shows when no solution exists
- ✅ Clear Display: Visual representation of the sequence
- ✅ 100% Accurate: Precise mathematical calculations
- ✅ Completely Free: No registration required
Understanding Consecutive Integers
Consecutive integers are whole numbers that follow each other in order, differing by 1.
- Examples: 5, 6, 7 or -3, -2, -1 or 10, 11, 12, 13
- Can be positive, negative, or include zero
- Spacing is always exactly 1 unit
- Not all sums can be represented by consecutive integers
Real-World Applications
Word Problems: "Find three consecutive integers whose sum is 45" → 14, 15, 16.
Geometry: Find consecutive integer side lengths that add to a perimeter.
Games: Solve puzzles involving consecutive number patterns.
Tips for Using This Calculator
- Not all sums have a solution - calculator will alert you
- Count must be at least 2 consecutive integers
- Solutions include negative numbers when appropriate
- Can verify solutions by adding the displayed numbers
Frequently Asked Questions
What are consecutive integers?
Consecutive integers are whole numbers in sequence, each differing by 1. Examples: 7, 8, 9 or -2, -1, 0, 1, 2.
What if no solution exists?
Not all sums can be represented by consecutive integers. The calculator will alert you when no whole number solution exists.
Can consecutive integers include negative numbers?
Yes! Consecutive integers can be negative, positive, or include zero. For example: -3, -2, -1, 0.
What's the minimum number of consecutive integers?
You need at least 2 consecutive integers. Most problems use 3 or more.