Table of Contents
What are Consecutive Numbers?
To understand the concept of consecutive numbers, we need to know that the number is written immediately before a number is called its predecessor. The number that is written just next to the other number is called the successor. For instance, let us consider the list of natural numbers,1, 2, 3, 4, and 5. The predecessor of 3 is 2, and the successor of 4 is 5. Consecutive numbers follow each other in their respective groups, from the smallest to the largest in the entire number system. Consecutive numbers usually have a difference of 1 between every two successive numbers.
Consecutive Even Numbers:
We all know what numbers are, even numbers. Now let us consider the set of even numbers from 4 to 18 and write them in their ascending order. The numbers are ordered as 4, 6, 8, 10, 12, 14, 16, 18 when written from the smallest to the largest numbers. We can see that the difference between any predecessor and successor pair is only 2.
Consecutive Odd Numbers:
Similarly, odd numbers are one less or one more than the even numbers. When we arrange them in their ascending order, we can see that the numbers are always 2. For example, take the numbers 5, 7, 9. These are called consecutive odd numbers because the difference between these given predecessor and successor pairs is only 2.
Tips for Consecutive Numbers:
- To find the missing numbers in a given set, students should write the numbers in their ascending order and find the difference between the predecessor and successor pair.
- If students denote the first number as n, then the consecutive numbers in the order will be n+1, n+2, n+3, n+4, and so on.
- If students denote the first integer as n, then the consecutive even integers or consecutive odd integers will be denoted as n+2, n+4, n+6, and so on.
- For an odd consecutive number, the general formula is 2n+1
- For an even consecutive number, the general formula is 2n.
Introduction to Integers
The term “integer” was derived in Mathematics from the Latin word “integer,” which means intact or complete. Integers are very much like whole numbers, but they also include negative numbers in their sets.
What is an Integer?
An integer is a number with no decimal or fractions included in its sets. They include negative and positive numbers and zero. Examples of integers are: -5, 0, 1, 5, 8, 97, and 3,06773.
A set of integers, which is represented by the capital letter Z, includes:
- Positive Integers: An integer is positive if it succeeds the number zero and is on the right side of the number line. Example: 1, 2, 3 . . .
- Negative Integers: An integer is negative if it is lesser than zero and is on the left side of the number line. Example: -1, -2, -3 . . .
- Zero is neither a negative integer nor a positive integer but is a whole number.
Rules of Integers
- Sum of the two positive integers: integer.
- Sum of the two negative integers: integer.
- Product of the two positive integers: integer.
- Product of the two negative integers: integer.
- Addition operation between any two integers and its inverse negative value will give the result of zero.
- The Multiplication method between any integer and it is reciprocal will give the result as one.
Properties of Integers
The fundamental properties of Integers are:
- Closure Property
- Associative Property
- Commutative Property
- Distributive Property
- Additive Inverse Property
- Multiplicative Inverse Property
- Identity Property
Consecutive numbers and integers are two significant and vital topics in mathematics. Although these topics are elementary and easy, students can get a deeper understanding of these topics through online classes like Cuemath online classes which help students understand the topics in detail. Cuemath will help students to strengthen their basic knowledge and will challenge them to solve complex problems.