Consecutive Integers Calculator
Find consecutive integers with given sum or product properties
Find Consecutive Integers
Number between 2 and 20
The desired sum value
Results
Step-by-Step Solution
Example Calculations
Sum Example
Problem: Find three consecutive integers whose sum is 42
Solution: Let x be the smallest integer
Then: x + (x+1) + (x+2) = 42
Simplifying: 3x + 3 = 42
Solving: 3x = 39, so x = 13
Answer: 13, 14, 15
Verification: 13 + 14 + 15 = 42 ✓
Product Example
Problem: Find two consecutive odd integers whose product is 63
Solution: Let the integers be (2x+1) and (2x+3)
Then: (2x+1)(2x+3) = 63
Expanding: 4x² + 8x + 3 = 63
Simplifying: 4x² + 8x - 60 = 0
Dividing by 4: x² + 2x - 15 = 0
Factoring: (x+5)(x-3) = 0
Solutions: x = -5 or x = 3
Answers: (-9, -7) or (7, 9)
Verification: (-9) × (-7) = 63 ✓ and 7 × 9 = 63 ✓
Consecutive Integer Formulas
Any Integers
Sequence: x, x+1, x+2, ...
Sum of n integers = nx + n(n-1)/2
Even Integers
Sequence: 2x, 2x+2, 2x+4, ...
Sum = 2nx + n(n-1)
Odd Integers
Sequence: 2x+1, 2x+3, 2x+5, ...
Sum = 2nx + n²
Properties & Tips
Consecutive integers differ by 1
Consecutive even/odd integers differ by 2
Sum problems usually have simpler solutions than products
Product problems may have multiple solutions or no solutions
Always verify your answer by checking the calculation
Understanding Consecutive Integers
What are Consecutive Integers?
Consecutive integers are whole numbers that follow each other in sequence without any gaps. For example, 5, 6, 7 are three consecutive integers, and -3, -2, -1, 0, 1 are five consecutive integers.
Types of Consecutive Integers
- •Any integers: ..., -2, -1, 0, 1, 2, 3, ...
- •Even integers: ..., -4, -2, 0, 2, 4, 6, ...
- •Odd integers: ..., -5, -3, -1, 1, 3, 5, ...
Common Applications
- •Finding numbers with specific sum properties
- •Solving algebra word problems
- •Number theory and mathematical proofs
- •Pattern recognition in sequences
Tip: When solving consecutive integer problems, always set up an equation using a variable to represent the smallest (or any) integer in the sequence.