1. What Are Consecutive Integers?

Consecutive integers are integers that follow each other in order without gaps. For example, 5, 6, 7 are three consecutive integers. Each consecutive integer is 1 more than the previous integer.

2. How To Calculate Consecutive Integers

The formula for consecutive integers is simple:

Where:

• \( n \) — The starting integer
• Each subsequent integer increases by 1

Example: If n = 10, the next 3 consecutive integers would be 11, 12, 13.

3. Applications of Consecutive Integers

Details: Consecutive integers are used in various mathematical problems, including:

• Algebra problems involving sums or products of consecutive numbers
• Number theory problems
• Real-world applications like numbering items or sequential events

4. Using the Calculator

Tips:

• Enter your starting integer (can be positive, negative, or zero)
• Specify how many consecutive integers you want to generate (max 20)
• The calculator will display the sequence of consecutive integers

5. Frequently Asked Questions (FAQ)

Q1: Can consecutive integers be negative?
A: Yes, consecutive integers can be negative (e.g., -3, -2, -1, 0, 1).

Q2: What's the difference between consecutive integers and consecutive even/odd integers?
A: Consecutive integers increase by 1 (5,6,7), while consecutive even/odd integers increase by 2 (2,4,6 or 5,7,9).

Q3: How are consecutive integers used in algebra?
A: They're often used in problems where you need to find numbers with certain properties (e.g., "Find three consecutive integers whose sum is 45").

Q4: Can the calculator handle large numbers?
A: Yes, within the limits of integer storage in PHP (typically ±2 billion).

Q5: What's the maximum number of integers I can generate?
A: The calculator is limited to 20 consecutive integers for practical display purposes.