Consecutive Numbers are the numbers that are next to each other in a queue. These numbers always consist of a difference of 1. The first step to understanding consecutive numbers is to be familiar with the number system.
In mathematics, numbers that sequentially follow one another from smallest to largest are known as consecutive numbers. This means that each number in the sequence is followed immediately by the next number without any gaps. For example, the consecutive numbers from 1 to 8 are 1, 2, 3, 4, 5, 6, 7, and 8.
In this article, we will understand the definition of consecutive numbers in maths followed by some basic examples, consecutive numbers from 1 to 100, their types, properties, formulas, how to find consecutive numbers, etc.
What are Consecutive Numbers?
Consecutive Numbers in maths are those numbers that are present in a sequential manner in increasing order. We can also understand consecutive numbers through the concept of predecessor and successor.
The number preceding another number is called its predecessor, while the number following it is called its successor.
Consecutive Numbers Meaning
The numbers that follow one another in ascending order are called consecutive numbers. In other words, we can say that the numbers which have the same difference between them are known as consecutive numbers.
Consecutive Numbers Examples
Suppose there is a series of numbers i.e. 1, 2, 3, 4, 5, 6 . . . These numbers have the same difference between them. Each number has a difference of 1. So these all are consecutive numbers.
According to another concept, if we took the number "3" from this series. The predecessor of 3 is 2 while its successor is 4. Here the difference between 3-2 = 1 and 4-3 = 1 is also the same. In this way, it is also proved that these are consecutive numbers.
The idea of successor and predecessor is very important in finding Consecutive Numbers. So now let's begin with Successor and Predecessor.
Successor and Predecessor
Idea of successors and predecessors, helps us understand numbers that come one after the other. Let's take a look at natural numbers as an example.
Natural numbers are 1, 2, 3, 4, 5, 6,...
- The successor of a number is the number that is one greater than the previous number, i.e. successor of n is n+1
- The predecessor of a number is the number that is one lesser than the next number, i.e. predecessor of n is n-1
Thus, consecutive numbers are found using the concept of successor.
Consecutive Numbers 1 to 100
Consecutive Numbers refers to the numbers that are written from 1 to 100 continuously. The chart below shows consecutive numbers from 1 to 100:

Types of Consecutive Numbers
In this section, we will learn about different kind of consecutive numbers. Consecutive numbers consists some types which helps us to differentiate. These are classified mainly into 3 categories:
Consecutive Natural Numbers
To understand consecutive natural numbers, we have to understand natural numbers first. We use natural numbers for normal counting.
In simple words, all whole numbers are natural numbers except zero (0). Natural consecutive numbers are those arranged in ascending order from small to large numbers.
For example: The natural consecutive numbers from 1 to 10 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Consecutive Even Numbers
Even numbers are the numbers which can be divided by 2. So the even numbers in which there is a difference of 2, are considered as Even Consecutive Numbers.
For example: The even consecutive numbers from 1 to 20 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. In this sequence the difference between each number is 2 and they all can be divided by 2, so these are called Consecutive Even Numbers.
Consecutive Odd Numbers
Odd numbers are those numbers which can't be divide by 2. The odd consecutive numbers also have a difference of 2 between them but they can't be divisible by 2. This is the main difference between even and Odd Consecutive Numbers.
Consecutive Integers
In consecutive numbers, we can only take numbers starting from 1. Consecutive integers are those integers which have both negative and positive set of numbers of numbers scale. These are of two types:
- Positive consecutive integers: 0, 1, 2, 3, 4, 5, 6.....
- Negative consecutive integers: -1, -2, -3, -4, -5, -6....
Properties of Consecutive Numbers
In this section, we will learn some basic properties of consecutive numbers which will help us to deeply understand the topic and we can easily solve the problems related to consecutive numbers.
- There should always be a fixed difference between any two consecutive numbers. Any two odd consecutive numbers will always have a difference of 2. Similarly, any two even consecutive numbers will also have a difference of 2.
- If two odd consecutive numbers are added, their addition will always be an even number. Similarly when any two even consecutive numbers are summed up, they will always give an even number. While adding two consecutive numbers, it will always give an odd number.
- If a sequence is made up of odd numbers, their sum will always be divisible by the total number 'n'
- HCF of Two Consecutive Numbers is always 1.
HCF of Two Consecutive Numbers
HCF means "Highest Common Factor". The greatest factor which is common between two or more than two numbers is called HCF. HCF is the common factor that can divide those numbers.
HCF of two consecutive numbers is always 1 as one(1) is the only common factor between any two consecutive numbers.
For example: A series of two consecutive numbers is given as 56, 57.. In this series the common factor between 56 and 57 is only 1. Therefore the HCF of two consecutive numbers 56 and 57 is 1.
To find the consecutive numbers, some formulas are used. These formulas help us to find the series of consecutive numbers.
As we know that, integers always follow a sequence and the difference between two consecutive integers is always equal to 1.
- For any integer n, the formula to get a consecutive integer is (n + 1)
For natural consecutive numbers, suppose 'a' is an integer. Now, to find the next numbers, simply use the formula a+1, a+2, a+3....In this way, we can easily find an order of numbers. Suppose 'a' is given as 6. Now add 6+1= 7, 6+2= 8, 6+3= 9...So, the consecutive number sequence is 6, 7, 8, 9.....and so on. Just keep adding consecutive numbers in the original number.
Natural Consecutive Numbers = a, a+1, a+2 . . .
Similarly, we represent consecutive even integers as '2a'. To find the next even consecutive numbers, simply add even consecutive numbers to 2a as 2a+2, 2a+4, 2a+6 and so on because even consecutive numbers have a difference of 2. Now, if the value of 'a' is 7 then 2a= 2×7= 14. Now add 14+2= 16, 14+4= 18, 14+6= 20 etc. The even consecutive series is 14, 16, 18, 20....and so on.
Even Consecutive Numbers: 2a, 2a+2, 2a+4 . . .
While in the case of consecutive odd integers, we represent it as '2a+1'. Now, the next odd consecutive integers will be 2a+3, 2a+5, 2a+7 etc. due to the difference of 2. Here, we take the value of 'a' is 3 which will give 2×3+1 = 7. Now kept adding to find next odd numbers as 2×3+3 = 9, 2×3+5 = 11, 2×3+7 = 13.... and so on.
Odd Consecutive Numbers: 2a+1, 2a+3, 2a+5 . . .
The formulas for consecutive numbers are summarized below:
Consecutive Numbers | Formulas |
---|
Natural Consecutive Numbers | a, a+1, a+2 . . . |
Even Consecutive Numbers | 2a, 2a+2, 2a+4 . . . |
Odd Consecutive Numbers | 2a+1, 2a+3, 2a+5 . . . |
Sum of Consecutive Numbers
We have studied earlier that a consecutive number always differs by the same value i.e. 1. Now, in this section, we will learn about performing the addition of two or more than two consecutive numbers.
To find the sum of consecutive numbers, a simple formula is used. The formula to add 'n' number of consecutive integers is:
Sum of 'n' consecutive numbers= n/2 ( first term + last term)
where,
- n is count of number of consecutive terms under consideration
- n = last term - first term + 1
Example: Find the sum of consecutive integers from 20 to 30.
Solution:
Sum of n consecutive numbers= n/2 ( 1st term + last term)
here, first term is 20 and last term is 30. First find n= 30-20+1= 11. Now, use the formula:
Sum of Consecutive Integers= 11/2 (20+30) = 11/2(50)= 11×25= 275.
Let's learn Sum of Consecutive Numbers Formula for different numbers.
Sum of Consecutive Natural Numbers
The formula for calculating the addition of consecutive natural numbers is:
Sum of Consecutive Natural Numbers= n(n+1)/2
Here,
- n = last natural number
- n+1 = next natural number
Example: Determine the sum of first 10 natural numbers. The first 10 natural numbers are (1, 2, 3, 4, 5, 6 ,7 ,8 9, 10).
Solution:
The last natural number is '10'.
sum of consecutive natural numbers= (10(10+1))/2= (10×11)/2= 110/2= 55.
Sum of Consecutive Even Numbers
To evaluate the sum of consecutive even numbers, the formula is:
Sum of Even Consecutive Numbers = n(n+1)
Example: Calculate the sum of first 3 even consecutive numbers.
Solution:
Given even term is '3'. The first 3 even consecutive numbers are 2,4 and 6.
sum of even consecutive numbers= 3(3+1)= 3×4= 12.
Sum of Odd Consecutive Numbers
The formula for finding the addition of consecutive odd numbers is:
Sum of Odd Consecutive Numbers = n2
Example: Find out the sum of first 6 odd consecutive numbers.
Solution:
The value of 'n' is '6'. The first 6 odd consecutive numbers will be (1, 3, 5, 7, 9, 11).
sum of consecutive odd numbers = (6)2 = 36.
How to Find Consecutive Numbers when Sum is Given?
To find consecutive numbers when sum is given is explained in the example added below,
Example: Find three consecutive numbers when the sum of these three numbers is 24.
Let, the three consecutive numbers are, (n -1), n, (n + 1)
Given, sum of number = 24
(n -1) + (n) + (n + 1) = 24
n + n + n - 1 + 1 = 24
3n = 24
n = 24/3 = 8
Thus, the three consecutive number are,
- n - 1 = 8 - 1 = 7
- n = 8
- n + 1 = 8 + 1 = 9
People Also Read:
Sample Problems on Consecutive Numbers
Here are some sample examples related to consecutive numbers:
Example 1: Find the value of integers, if the sum of two consecutive integers is 41?
Solution:
Let two consecutive numbers be z and z+1
Given that:
z+ (z+1)= 41
2z + 1 = 41
2z = 41-1
z = 40/2
z = 20 and z+1= 20+1= 21
Hence, the consecutive integers whose sum is 41 are 20 and 21.
Example 2: If two consecutive odd numbers have a sum of 92. Find the numbers?
Solution:
Suppose two consecutive odd numbers are n and n+2 since the odd consecutive numbers differ by 2.
Given that:
n+ (n+2)= 92
⇒ 2n+2= 92
⇒ 2n= 92-2
⇒ n= 90/2
⇒ n= 45 and n+2= 45+2= 47
Therefore, the two consecutive odd numbers whose sum is 92 are 45 and 47.
Example 3: Find the Sum of First 50 Natural Numbers.
Solution:
Since, n = 50
We know that sum of first 'n' natural numbers = n(n + 1)/2
Hence, Sum of First 50 natural numbers (50 × 51)/2 = 25 × 51 = 1275
Example 4: Find three consecutive integers such that the sum of the second and third integers is 31.
Solution:
Let the three consecutive integers be x, x+1, and x+2.
Given that the sum of the second and third integers is 31: (x+1)+(x+2)=31
Simplifying: 2x+3=31
Subtract 3 from both sides: 2x=28
Divide by 2: x=14
So the three consecutive integers are x=14, x+1 = 15, and x+2=16.
Example 5: The sum of four consecutive even numbers is 100. Find the numbers.
Solution:
Let the four consecutive even numbers be y, y+2, y+4, and y+6.
Given that the sum of these numbers is 100: y+(y+2)+(y+4)+(y+6)=100
Simplifying: 4y+12=100
Subtract 12 from both sides: 4y=88
Divide by 4: y=22
So the four consecutive even numbers are y=22, y+2=24, y+4=26, and y+6=28.
Practice Problems on Consecutive Numbers
After understanding consecutive numbers and learning its important properties and formulas, now it's time to practice some questions of consecutive numbers to strengthen the topic more. These are few practice questions which will help you to revise your concept:
Problem 1: If the product of any four consecutive numbers is 32,760. Find those numbers?
Problem 2: Jenny writes 3 consecutive numbers on a paper. The sum of these is 150. What are the numbers that Jenny wrote on the paper?
Problem 3: Find the even consecutive numbers starting from 50 to 70?
Problem 4: The HCF of two consecutive odd numbers is 45. Solve the question and find the numbers.
Problem 5: Three consecutive even numbers are given in which the sum of the first two is 26. Find those numbers?
Problem 6: The sum of four consecutive odd numbers is 80. What are those numbers?
Problem 7: Find three consecutive multiples of 7 whose sum is 168.
Problem 8: The difference between the square of two consecutive even numbers is 36. What are those numbers?
Problem 9: The sum of the first and last numbers of five consecutive numbers is 62. Find the numbers.
Problem 10: If the sum of three consecutive odd numbers is 75, what are the numbers?
Conclusion of Consecutive Numbers in Maths
Consecutive numbers play a fundamental role in mathematics, providing a simple yet powerful way to understand sequences and numerical patterns. These numbers, which follow each other in order without gaps, are used in various mathematical concepts, including arithmetic operations, algebra, and number theory. Recognizing and working with consecutive numbers help in solving problems related to series, progressions, and even real-life situations.
Similar Reads
Maths Mathematics, often referred to as "math" for short. It is the study of numbers, quantities, shapes, structures, patterns, and relationships. It is a fundamental subject that explores the logical reasoning and systematic approach to solving problems. Mathematics is used extensively in various fields
5 min read
Basic Arithmetic
What are Numbers?Numbers are symbols we use to count, measure, and describe things. They are everywhere in our daily lives and help us understand and organize the world.Numbers are like tools that help us:Count how many things there are (e.g., 1 apple, 3 pencils).Measure things (e.g., 5 meters, 10 kilograms).Show or
15+ min read
Arithmetic OperationsArithmetic Operations are the basic mathematical operationsâAddition, Subtraction, Multiplication, and Divisionâused for calculations. These operations form the foundation of mathematics and are essential in daily life, such as sharing items, calculating bills, solving time and work problems, and in
9 min read
Fractions - Definition, Types and ExamplesFractions are numerical expressions used to represent parts of a whole or ratios between quantities. They consist of a numerator (the top number), indicating how many parts are considered, and a denominator (the bottom number), showing the total number of equal parts the whole is divided into. For E
7 min read
What are Decimals?Decimals are numbers that use a decimal point to separate the whole number part from the fractional part. This system helps represent values between whole numbers, making it easier to express and measure smaller quantities. Each digit after the decimal point represents a specific place value, like t
10 min read
ExponentsExponents are a way to show that a number (base) is multiplied by itself many times. It's written as a small number (called the exponent) to the top right of the base number.Think of exponents as a shortcut for repeated multiplication:23 means 2 x 2 x 2 = 8 52 means 5 x 5 = 25So instead of writing t
9 min read
PercentageIn mathematics, a percentage is a figure or ratio that signifies a fraction out of 100, i.e., A fraction whose denominator is 100 is called a Percent. In all the fractions where the denominator is 100, we can remove the denominator and put the % sign.For example, the fraction 23/100 can be written a
5 min read
Algebra
Variable in MathsA variable is like a placeholder or a box that can hold different values. In math, it's often represented by a letter, like x or y. The value of a variable can change depending on the situation. For example, if you have the equation y = 2x + 3, the value of y depends on the value of x. So, if you ch
5 min read
Polynomials| Degree | Types | Properties and ExamplesPolynomials are mathematical expressions made up of variables (often represented by letters like x, y, etc.), constants (like numbers), and exponents (which are non-negative integers). These expressions are combined using addition, subtraction, and multiplication operations.A polynomial can have one
9 min read
CoefficientA coefficient is a number that multiplies a variable in a mathematical expression. It tells you how much of that variable you have. For example, in the term 5x, the coefficient is 5 â it means 5 times the variable x.Coefficients can be positive, negative, or zero. Algebraic EquationA coefficient is
8 min read
Algebraic IdentitiesAlgebraic Identities are fundamental equations in algebra where the left-hand side of the equation is always equal to the right-hand side, regardless of the values of the variables involved. These identities play a crucial role in simplifying algebraic computations and are essential for solving vari
14 min read
Properties of Algebraic OperationsAlgebraic operations are mathematical processes that involve the manipulation of numbers, variables, and symbols to produce new results or expressions. The basic algebraic operations are:Addition ( + ): The process of combining two or more numbers to get a sum. For example, 3 + 5 = 8.Subtraction (â)
3 min read
Geometry
Lines and AnglesLines and Angles are the basic terms used in geometry. They provide a base for understanding all the concepts of geometry. We define a line as a 1-D figure that can be extended to infinity in opposite directions, whereas an angle is defined as the opening created by joining two or more lines. An ang
9 min read
Geometric Shapes in MathsGeometric shapes are mathematical figures that represent the forms of objects in the real world. These shapes have defined boundaries, angles, and surfaces, and are fundamental to understanding geometry. Geometric shapes can be categorized into two main types based on their dimensions:2D Shapes (Two
2 min read
Area and Perimeter of Shapes | Formula and ExamplesArea and Perimeter are the two fundamental properties related to 2-dimensional shapes. Defining the size of the shape and the length of its boundary. By learning about the areas of 2D shapes, we can easily determine the surface areas of 3D bodies and the perimeter helps us to calculate the length of
10 min read
Surface Areas and VolumesSurface Area and Volume are two fundamental properties of a three-dimensional (3D) shape that help us understand and measure the space they occupy and their outer surfaces.Knowing how to determine surface area and volumes can be incredibly practical and handy in cases where you want to calculate the
10 min read
Points, Lines and PlanesPoints, Lines, and Planes are basic terms used in Geometry that have a specific meaning and are used to define the basis of geometry. We define a point as a location in 3-D or 2-D space that is represented using coordinates. We define a line as a geometrical figure that is extended in both direction
14 min read
Coordinate Axes and Coordinate Planes in 3D spaceIn a plane, we know that we need two mutually perpendicular lines to locate the position of a point. These lines are called coordinate axes of the plane and the plane is usually called the Cartesian plane. But in real life, we do not have such a plane. In real life, we need some extra information su
6 min read
Trigonometry & Vector Algebra
Trigonometric RatiosThere are three sides of a triangle Hypotenuse, Adjacent, and Opposite. The ratios between these sides based on the angle between them is called Trigonometric Ratio. The six trigonometric ratios are: sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).As give
4 min read
Trigonometric Equations | Definition, Examples & How to SolveTrigonometric equations are mathematical expressions that involve trigonometric functions (such as sine, cosine, tangent, etc.) and are set equal to a value. The goal is to find the values of the variable (usually an angle) that satisfy the equation.For example, a simple trigonometric equation might
9 min read
Trigonometric IdentitiesTrigonometric identities play an important role in simplifying expressions and solving equations involving trigonometric functions. These identities, which include relationships between angles and sides of triangles, are widely used in fields like geometry, engineering, and physics. Some important t
10 min read
Trigonometric FunctionsTrigonometric Functions, often simply called trig functions, are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides.Trigonometric functions are the basic functions used in trigonometry and they are used for solving various types of problems in
6 min read
Inverse Trigonometric Functions | Definition, Formula, Types and Examples Inverse trigonometric functions are the inverse functions of basic trigonometric functions. In mathematics, inverse trigonometric functions are also known as arcus functions or anti-trigonometric functions. The inverse trigonometric functions are the inverse functions of basic trigonometric function
11 min read
Inverse Trigonometric IdentitiesInverse trigonometric functions are also known as arcus functions or anti-trigonometric functions. These functions are the inverse functions of basic trigonometric functions, i.e., sine, cosine, tangent, cosecant, secant, and cotangent. It is used to find the angles with any trigonometric ratio. Inv
9 min read
Calculus
Introduction to Differential CalculusDifferential calculus is a branch of calculus that deals with the study of rates of change of functions and the behaviour of these functions in response to infinitesimal changes in their independent variables.Some of the prerequisites for Differential Calculus include:Independent and Dependent Varia
6 min read
Limits in CalculusIn mathematics, a limit is a fundamental concept that describes the behaviour of a function or sequence as its input approaches a particular value. Limits are used in calculus to define derivatives, continuity, and integrals, and they are defined as the approaching value of the function with the inp
12 min read
Continuity of FunctionsContinuity of functions is an important unit of Calculus as it forms the base and it helps us further to prove whether a function is differentiable or not. A continuous function is a function which when drawn on a paper does not have a break. The continuity can also be proved using the concept of li
13 min read
DifferentiationDifferentiation in mathematics refers to the process of finding the derivative of a function, which involves determining the rate of change of a function with respect to its variables.In simple terms, it is a way of finding how things change. Imagine you're driving a car and looking at how your spee
2 min read
Differentiability of a Function | Class 12 MathsContinuity or continuous which means, "a function is continuous at its domain if its graph is a curve without breaks or jumps". A function is continuous at a point in its domain if its graph does not have breaks or jumps in the immediate neighborhood of the point. Continuity at a Point: A function f
11 min read
IntegrationIntegration, in simple terms, is a way to add up small pieces to find the total of something, especially when those pieces are changing or not uniform.Imagine you have a car driving along a road, and its speed changes over time. At some moments, it's going faster; at other moments, it's slower. If y
3 min read
Probability and Statistics
Basic Concepts of ProbabilityProbability is defined as the likelihood of the occurrence of any event. It is expressed as a number between 0 and 1, where 0 is the probability of an impossible event and 1 is the probability of a sure event.Concepts of Probability are used in various real life scenarios : Stock Market : Investors
7 min read
Bayes' TheoremBayes' Theorem is a mathematical formula used to determine the conditional probability of an event based on prior knowledge and new evidence. It adjusts probabilities when new information comes in and helps make better decisions in uncertain situations.Bayes' Theorem helps us update probabilities ba
13 min read
Probability Distribution - Function, Formula, TableA probability distribution is a mathematical function or rule that describes how the probabilities of different outcomes are assigned to the possible values of a random variable. It provides a way of modeling the likelihood of each outcome in a random experiment.While a Frequency Distribution shows
13 min read
Descriptive StatisticStatistics is the foundation of data science. Descriptive statistics are simple tools that help us understand and summarize data. They show the basic features of a dataset, like the average, highest and lowest values and how spread out the numbers are. It's the first step in making sense of informat
5 min read
What is Inferential Statistics?Inferential statistics is an important tool that allows us to make predictions and conclusions about a population based on sample data. Unlike descriptive statistics, which only summarize data, inferential statistics let us test hypotheses, make estimates, and measure the uncertainty about our predi
7 min read
Measures of Central Tendency in StatisticsCentral tendencies in statistics are numerical values that represent the middle or typical value of a dataset. Also known as averages, they provide a summary of the entire data, making it easier to understand the overall pattern or behavior. These values are useful because they capture the essence o
11 min read
Set TheorySet theory is a branch of mathematics that deals with collections of objects, called sets. A set is simply a collection of distinct elements, such as numbers, letters, or even everyday objects, that share a common property or rule.Example of SetsSome examples of sets include:A set of fruits: {apple,
3 min read
Practice