#Consecutive natural numbers series

Let us solve an example to understand this better.Įxample: Find three consecutive integers such that their sum is 51.

Generally, we find three consecutive integers given with a certain condition to solve problems based on consecutive integers. Three consecutive integers are a sequence of three integers such that their difference is fixed. So, x = 13.Īnswer: The required consecutive positive integers are 13 and 14.

Since, we need a positive integer, x = -14 is rejected. Solution: Assume one integer to be x, then the other integer is x + 1, as the difference between two consecutive positive integers is 1. Let us solve an example related to the concept for a better understanding.Įxample: Find two consecutive positive integers sum of whose squares is 365. We can have various sequences of consecutive positive integers such as consecutive even positive integers and consecutive odd positive integers. are consecutive positive integers with a fixed difference equal to 1. Similarly, the sum of any 15 consecutive odd numbers is always divisible by 15.Ĭonsecutive positive integers are a sequence of natural numbers with a fixed difference. For example, if we take the sum of any 2 consecutive odd numbers, then their sum will always be divisible by 2. The sum of 'n' consecutive odd integers is always divisible by 'n'.For example, if we make a list of consecutive even integers, -4, -2, 0, 2, 6, 8, 10, 12, and so on, we see that the difference between each successive integer is 2. The difference between each consecutive even integer is always 2.For example, if we make a list of consecutive odd integers, -3, -1, 1, 3, 5, 7, and so on, we see that the difference between each successive integer is 2. The difference between each consecutive odd integer is always 2.

#Consecutive natural numbers series

Therefore, if we take the first integer to be 'x', the series can be written as, x, x +1, x + 2, x + 3, and so on. We can see that the difference between each successive number is 1. For example, let us observe the following list: -2, -1, 0, 1, 2. The difference between each consecutive integer in a sequence is the same.Let us note the properties of consecutive integers. 1.Ĭonsecutive integers are those integers that follow each other in ascending order. We will also go through some solved examples for a better understanding of the concept. We shall also learn to determine the sum of three consecutive integers and consecutive positive integers. In this article, we will explore the concept of consecutive integers, consecutive even and odd integers with examples, and their formula properties. The consecutive integers formula helps in finding such integers for any given number or to check whether a set of integers are consecutive or not. The consecutive integers are integers that follow each other in increasing order. While listing consecutive integers in a sequence, no numbers are skipped in between and that is the reason why the difference between them is always fixed. Consecutive integers are those integers that follow each other in a regular counting pattern.