Consecutive Numbers

Consecutive numbers are numbers that follow each other in order, with a difference of 1 between each pair of numbers. For example, 3, 4, and 5 are consecutive numbers because they are in order and the difference between each pair is 1.

Properties of Consecutive Numbers

1. Odd and Even Numbers: If one of the consecutive numbers is even, the next one is odd, and vice versa.
2. Sum and Average: The sum of consecutive numbers can be found by multiplying the average of the numbers by the total count of numbers.
3. Algebraic Representation: Consecutive numbers can be represented algebraically as x, x+1, x+2, etc., where x is the first number.

Examples

Example 1: Find three consecutive numbers if the sum of the first two is 25.

Let the first number be x. The next two consecutive numbers are x+1 and x+2. Given that the sum of the first two numbers is 25, we have the equation:

x + (x+1) = 25

Solving for x, we get x = 12. So, the consecutive numbers are 12, 13, and 14.

Example 2: The average of three consecutive numbers is 15. Find the numbers.

Let the first number be x. The next two consecutive numbers are x+1 and x+2. Given that the average is 15, we have the equation:

(x + x+1 + x+2)/3 = 15

Solving for x, we get x = 14. So, the consecutive numbers are 14, 15, and 16.

Study Guide

When working with consecutive numbers, remember the following key points:

• Consecutive numbers follow each other in order with a difference of 1 between each pair of numbers.
• If one of the consecutive numbers is even, the next one is odd, and vice versa.
• The sum of consecutive numbers can be found by multiplying the average of the numbers by the total count of numbers.
• Algebraically, consecutive numbers can be represented as x, x+1, x+2, etc., where x is the first number.

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