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# Consecutive Integers

Integers do not contain fractional or decimal portion. Integers include all positive natural numbers, zero and negative of all natural numbers. The set of integers is represented by
$\mathbb{Z}$ = { ..., -3, -2, -1, 0, 1, 2, 3, ...}

Consecutive Integers
Consecutive integers are the integers which come one after another with a difference of "1". In other words, we can say that the set of consecutive integers is a sequence of integers which have a difference of 1 among one another. It means, in consecutive integers, if a number is subtracted from its successive number, then result comes out to be "1".
The general sequence of consecutive numbers is given below:
n, n + 1, n + 2, n + 3, ...
where, n is an integer.
If we substitute any integer in the above sequence, we get consecutive integers.

For example: At n = 1, we get
1, 1 + 1, 1 + 2, 1 + 3, .... or 1, 2, 3, 4, ...
At n = -3, we get
-3, -3 + 1, -3 + 2, -3 + 3, .... or -3, -2, -1, 0, ...

Types of Consecutive Integers

There are two types of consecutive integers that are explained below:
• Even consecutive integers
• Odd consecutive integers

Even Consecutive Integers
The sequence of consecutive even integers is known as even consecutive integers. Here, the sequence starts with an even number and the difference between two continuous integers is "two". General term for even consecutive integers is:
2n, 2n + 2, 2n + 4, ...
Where, n is an integer.
If we substitute any integer, we get a sequence of even consecutive numbers.

For example: Putting n = 2, we get
4, 4 + 2, 4 + 4, 4 + 6, ... or 4, 6, 8, 10, ....
Putting n = 3, we get
6, 6 + 2, 6 + 4, 6 + 6, ... or 6, 8, 10, 12, ...

Odd Consecutive Integers
The sequence of consecutive odd integers is known as odd consecutive integers. Here, the sequence starts with an odd number and the difference between two continuous integers is "two". General term for even consecutive integers is:
2n + 1, 2n + 3, 2n + 5, ...
Where, n is an integer.
If we substitute any integer, we get a sequence of odd consecutive numbers.

For example: Putting n = 2, we get
4 + 1, 4 + 3, 4 + 5, 4 + 7, ... or 5, 7, 9, 11, ....
Putting n = -1, we get
-2 + 1, -2 + 3, -2 + 5, -2 + 7, ... or -1, 1, 3, 5, ...

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