Brief Explanation

Consecutive numbers are defined as a sequence of numbers in which each term follows the preceding one by a consistent interval.

Let n be an integer,

• Consecutive four integers are; n, n + 1, n + 2, n + 3

• Consecutive four even integers are; 2n, 2n + 2, 2n + 4, 2n + 6

• Consecutive four odd integers are; 2n + 1, 2n + 3, 2n + 5, 2n + 7

• Consecutive four integers divisible by three are; 3n, 3n + 3, 3n + 6, 3n + 9

The Sum Of Consecutive Numbers

Where $n$ is a counting number,

•   1+2+3+…..+n=   

•  The sum of consecutive positive even natural numbers, 2 + 4 + 6 + … + (2n) = n(n + 1)

• The sum of consecutive odd natural numbers, 1 + 3 + 5 + … + (2n – 1) = 

• The sum of consecutive integers with a common difference,  is expressed by the formula:

r+(r+x)+(r+2x)+…+n=(Number of Terms)⋅(Median Term) = 

$r$ represents the first term, $n$ the last term, and $x$ the common difference

Note: The sum of consecutive numbers with a common difference, when divided by the number of terms, yields the median term. If the number of terms is even, the median term does not belong to the number sequence.