Show Before understanding consecutive numbers, let us look into consecutive meanings in maths. Consecutive means following each other continuously in a series or a sequence. In Mathematics, numbers that follow each other in a series are termed consecutive numbers. Consecutive numbers meaning is “The numbers which continuously follow each other in the order from smallest to largest.” Consecutive Numbers Examples: Consecutive numbers from 1 to 8 are 1, 2, 3, 4, 5, 6, 7, and 8. Here, the difference between each number is 1. Consecutive numbers from 80 to 90 with differences as 2 are 80, 82, 84, 86, 88, and 90. Here, the difference between each number is 2. This type of consecutive number system where each number is an even number and the difference between each number is 2 is called consecutive even integers which we will discuss in detail in the latter part of this chapter. Consecutive numbers from -1 to 7 are -1, 0, 1, 2, 3, 4, 5, 6, and 7. Here, the difference between each number is 1. What does Consecutive Natural Numbers Mean?Natural numbers are the numbers that are used for counting and ordering. Natural numbers include all whole numbers except 0. In the mathematical form, the natural numbers are written as follows: N = {1, 2, 3, 4, 5, 6, 7, 8, 9, ……} So consecutive natural numbers are the numbers that continuously follow each other in order from the smallest number to the largest number. For example, the consecutive natural numbers from 10 to 15 are 10, 11, 12, 13, 14, and 15. The consecutive numbers from -5 to -1 are not consecutive natural numbers because these numbers don't fall under natural numbers. These numbers are integers. What is Meant by Consecutive Numbers with Even Integers?An even number is one that is divisible by two and leaves a 0 as a remainder. So Consecutive Numbers with Even integers or simply called consecutive even integers is a sequence where the numbers continuously follow each other in the order from the smallest number to the largest number with the difference between each number is 2 and each number is divisible by 2. Consecutive integers examples: 2, 4, 6, 8, 10, and 12 are consecutive even integers between the numbers 2 and 12. -8, -6, -4, and -2 are consecutive even integers between the numbers -8 and -2. What is Meant by Consecutive Numbers with Odd Integers?A number that is not divisible by 2 is called an odd number. In the case of an odd number, the remainder is always 1. So consecutive odd integers is a sequence where the numbers continuously follow each other in the order from the smallest number to the largest number with the difference between each number is 2 and each number not divisible by 2. Consecutive integers examples: The consecutive odd integers between 1 and 15 are 1, 3, 5, 7, 9, 11, 13, and 15. The consecutive odd integers between -11 and -1 are -11, -9, -7, -5, -3, and -1. Properties of Consecutive Numbers
5+7+9+11+13+15+17 = 77. 77/7 = 11 which satisfies this property.
Problems with Consecutive Numbers1) What is a consecutive number in maths for natural numbers between 1 and 25? Ans: The consecutive numbers for the natural numbers between 1 and 25 are as follows: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25. 2) Write the consecutive even integers between 20 and 40. Ans: The consecutive even integers between 20 and 40 are as follows: 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40. 3) Find the sum of two consecutive numbers 8 and 9. Ans: The sum of two consecutive numbers is 8+9 = 17. Important Concepts of Numbers and Consecutive Numbers
Conclusion
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Given: Average of 5 consecutive number = 21 Formula used: Average = (Sum of values)/(Number of values) Calculations: Let the numbers be x, x + 1, x + 2, x + 3, x + 4. Average = (x + x + 1 + x + 2 + x + 3 + x + 4)/5 ⇒ 21 = (5x + 10)/5 ⇒ 105 = 5x + 10 ⇒ 95 = 5x ⇒ x = 19 Highest number = x + 4 ⇒ 19 + 4 ⇒ 23. ∴ The highest number will be 23. India’s #1 Learning Platform Start Complete Exam Preparation
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