Consecutive Integers Formula

About Consecutive Integers Formula

In mathematics, you'll frequently encounter problem statements that ask you to find the sum or difference of two or more consecutive integers. The clause of these successive integers being odd or even is also inserted a few times. You must utilise a variable for one integer and then represent it in the form of its consecutive integers before simplifying the problem statement and generating its equation. Allow me to illustrate this with an example.

Assume you're looking for two consecutive numbers with a sum of 89. How do you approach this issue? You start with a variable, say x, whose value you don't know. After then, you must choose another number. The integer next to x will be (x + 1) because the problem demands two consecutive integers. The sum of x and (x+1) is now 89, as per the problem. This can be expressed as an equation: x + (x + 1) = 89. When we solve this equation, we get x = 44 and the next number (x + 1) = 45, for a total of 89.

Knowing the consecutive integer formula can also help you solve a variety of arithmetic difficulties.

Consecutive Integer Formula

If n is an integer, the next two integers will be (n + 1) and (n + 2). Let n be 1, for example. (1 + 1) and (1 + 2), or 2 and 3, are its consecutive numbers.

Hence, the formula:

n, n+1, n+2, n+3, ………..…

Even Consecutive Integer Formula

An even integer is written as 2n in mathematics. If 2n is an even number, the next two even numbers will be (2n + 2) and (2n + 4). Consider the number 2n, which is an even integer. Its successive integers are (4 + 2) and (4 + 4), or 6 and 8, respectively.

Hence, the formula:

2n, 2n+2, 2n+4, 2n+6, ………

It's important to note that the difference between two even consecutive integers is 2, else we'd end up with a non-even integer.

Odd Consecutive Integer Formula

In mathematics, an odd number is written as 2n + 1. If 2n + 1 is an odd number, the following two odd consecutive integers are (2n + 3) and (2n + 5). Consider the number 2n + 1, which is an odd integer. Its successive integers are (7 + 2) and (7 + 4), or 9 and 11, respectively.

Hence, the formula:

2n+1, 2n+3, 2n+5, 2n+7, …..…

It's worth noting that the difference between two odd consecutive integers is 2, else we'd wind up with an integer that's both consecutive and odd. To get all the Maths formulas check out the main page. 

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Consecutive Integers Formula
Consecutive Integers Formula

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