1. What Are Three Consecutive Integers?

Three consecutive integers are whole numbers that follow each other in order without gaps. For any integer n, the three consecutive integers are n-1, n, and n+1.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( n \) — The middle integer
• \( n-1 \) — The previous integer
• \( n+1 \) — The next integer

Explanation: This formula generates three numbers in sequence, each differing by 1 from its neighbors.

3. Applications of Consecutive Integers

Details: Consecutive integers are used in number theory, algebra problems, sequence analysis, and various mathematical proofs. They're particularly useful in solving word problems involving sequential numbers.

4. Using the Calculator

Tips: Simply enter the middle integer (n) and the calculator will display the three consecutive integers (n-1, n, n+1). The input must be a whole number (positive, negative, or zero).

5. Frequently Asked Questions (FAQ)

Q1: Can the integers be negative?
A: Yes, the calculator works with any integer, including negative numbers and zero.

Q2: What's the difference between consecutive integers and consecutive numbers?
A: Consecutive integers are specifically whole numbers that follow each other, while consecutive numbers could include decimals or fractions with a constant difference.

Q3: Can this calculator find consecutive even or odd integers?
A: No, this calculator only finds standard consecutive integers. For consecutive even or odd integers, the formula would be n-2, n, n+2.

Q4: What if I know the sum of three consecutive integers?
A: If you know the sum S, the middle number would be S/3, since (n-1)+n+(n+1) = 3n.

Q5: How are consecutive integers used in algebra?
A: They're often used in problems where you need to find unknown numbers that follow each other, especially in word problems about ages, page numbers, or sequential events.