While counting numbers naturally, we all just count the consecutive integers or consecutive numbers. Consecutive integers are those numbers that follow each other in a constant sequence. While counting several items to selecting a set of numbers and starting counting from the beginning of that set, we count the consecutive integers.
Consecutive integers follow a fixed sequence where the succeeding number is 1 more than the previous number. Consecutive numbers are represented as n, n+1,n+2, and so on, where n is an integer.
Let us look at 2 two sets of numbers. The first set is called consecutive positive integers and the second set is called consecutive negative integers.
Example 1: 7, 8, 9, 10, 11
Here we see a set of consecutive integers that are found by adding one to the next number, which is represented as the expression a+1, with a = 0, 1, 2, ….
Example 2: -3, -4, -5, -6, -7
Here we see a set of consecutive integers that is found by subtracting 1 from the next number, which is represented as the expression 1 - a, with a = 2, 3, 4, ….
There are two types of consecutive integers:
Even consecutive integers
Odd consecutive integers
Consecutive even integers formula is the set of numbers or integers that differs from the previous number by a difference of 2. Or we can say that each integer or number is divisible by 2.
The consecutive even integers formula is referred to as if, a is an even number, then a + 2, a + 4, a + 6, ... are the Even consecutive integers.
Example: 6, 8, 10, 12, .....
-6, -4, -2,....
140, 142, 144, 146…..
You can also represent consecutive even integers by 2a + 2, where a = 0, 1, 2, ….
Consecutive odd integers formula is the set of numbers or integers that differs from the previous number by a difference of 2. Each resultant integer is an odd number.
Consecutive odd integers formula is referred to as if it is an odd number, then a + 2, a + 4, a + 6 …... are consecutive odd integers.
Example: 1, 3, 5, 7, ....
-7, -5, -3, -1, ...
You can also represent consecutive odd integers by 2a + 2, where a = 0, 1, 2,….
So in general, the consecutive integers formula is expressed as a + 1
Whereas, the consecutive odd integers formula is expressed as 2a + 1, and the consecutive even integers formula is expressed as 2a.
Where “a” is any integer.
The consecutive numbers are sometimes used to frame word problems. The sum of the consecutive integers formula is always an odd number. Only a single accurate number is divisible by n in a set of consecutive integers. In a set of consecutive numbers, you can only find two even and two odd numbers. If “a” is an odd number, then the sum of consecutive integers is divisible by m.
1. How Many Digits can a Set of Consecutive Integers have in Maximum?
Ans: In a set of consecutive integers, there is no limit in the maximum count of the digits. If we consider two sets, 1, 2, 3, ...... and 996, 997, 988, 999, ….. then both these sets are termed as consecutive integers because they do not have any gaps which will break the number sequence.
2. If the Sum of Three Consecutive Integers is 99, Find out the Three Integers. Also, Find out the Product of the First and Third Integer.
Ans: Let say, that the three consecutive integers: x, x + 1, x + 2
According to the sum of consecutive integers formula,
x + x + 1 + x + 2 = 99
3x + 3 = 99
3x = 99 - 3
3x = 96
x = 96 ÷ 3
x = 32
x + 1 = 33
x + 2 = 34
The product of first and third integer = 33 × 34 = 1088
3. Explain with an Example What is Consecutive Even Integers Formula and Consecutive Odd Integers Formula.
Consecutive Even Integers Formula: Let 2 is an integer, then applying consecutive even integers formula, the set of even integers are:
n, n + 2, n + 4, n + 6, ...
= 2, 2 + 2, 2 + 4, 2 + 6, ….
= 2, 4, 6, 8, ....
Consecutive Even Integers Formula: Let 3 is an integer then applying consecutive odd integers formula the set of odd integers are:
n, n + 2, n + 4, n + 6, ...
= 3, 3 + 2, 3 + 4, 3 + 6, ....
= 3, 5, 7, 9, ....