Three Consecutive Integers
Product of three consecutive integers (apart from 0) is always divisible by 6 this is shown as, suppose we have three consecutive integers then they are represented as,
n, n + 1, n + 2
Now the product of these three integers is,
(n)(n +1)(n + 2) = n3 + 3n2 + 2n
The above expression is always divisible by 6 and can be proved using Mathematical Induction. Thus, we can say that product of three consecutive integers is always divisible by 6.
For example,
- 1 × 2 × 3 = 6 {Divisible by 6}
- 5 × 6 × 7 = 420 {Divisible by 6}
- 11 × 12 × 13 = 1716 {Divisible by 6}, etc
Consecutive Integers
Consecutive Integers are the integers that follow each other, i.e. while continuously writing integers they come next to each other. they have a difference of one(1). For example, …-3, -2, -1, 0, 1, 2, 3,… this is a sequence of consecutive integers. Apart from that natural numbers are also called consecutive integers because they are all integers and the difference between two consecutive natural numbers is always 1.
Thus, we can say that consecutive integers are the number that follows a regular pattern of writing and there is a fixed difference between any two consecutive integers, i.e. they have a difference of One(1). We represent any two consecutive integers as n, n + 1 where n ϵ Z.
In this article, we will learn about Consecutive Integers, Consecutive Even Integers, Consecutive Odd Integers, Examples, and others in detail.
Table of Content
- Consecutive Meaning
- What are Consecutive Integers?
- Examples of Consecutive Integers
- Consecutive Even Integers
- Consecutive Odd Integers
- Consecutive Integers Formula
- Consecutive Positive Integers
- Three Consecutive Integers
- Properties of Consecutive Integers
- Consecutive Integers Solved Examples
- Practice Questions on Consecutive Integers
Before learning in detail about Consecutive Integers let’s first understand what is the meaning of Consecutive in maths.