When we come across with numbers and its different types, we learn about integers. These are important type of numbers which include natural numbers, zero, and negative of natural numbers. In other words, integers are the superset of whole numbers and negative of all natural numbers. The set of integers is denoted by $\mathbb{Z}$. We can represent the set of integers in the following way :

Consecutive integers are represented by n, n+1, n+2..., where 'n' is any integer.

- Even consecutive integers
- Odd consecutive integers

Even consecutive numbers are those which start from 2 and are obtained by adding 2 successively, such as - 2, 4, 6, 8, 10, ....

On the other hand, odd consecutive number start from 3 and eventually can be obtained by adding 2, such as - 3, 5, 7, 9, ....

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When the continuous integer begins with an even number and the difference between the two numbers in the sequence is two.

Example for even consecutive integers are 12, 14, and 16

When the continuous integer begins with an odd number and the difference between the two numbers in the sequence is two.

Example for even consecutive integers are 13, 15, and 17

Here are some** c****onsecutive integers problems **-

Sum of the consecutive integers are 33.

Let the consecutive integers are (v), (v + 1), (v + 2)

By given data

(v) + (v + 1) + (v + 2) = 33

3 v + 3 = 33

3 v = 33 - 3

3 v = 30

v = $\frac{30}{3}$

v = 10

The algebra consecutive integers are

v =10

v + 1= 11

v + 2 = 12

The consecutive integers are 10, 11, and 12.

Sum of the even consecutive integers are 66.

Let the even consecutive integers are (v), (v+2), (v+4)

By given data

(v) + (v + 2) + (v + 4) = 66

3 v + 6 = 66

3 v = 66 - 6

3 v = 60

v = $\frac{60}{3}$

v = 20.

The algebra consecutive integers are

v =20

v + 2= 22

v + 4= 24

The consecutive integers are 20, 22, and 24.

Sum of two odd consecutive integers are 48

Let the odd consecutive integers are (x), (x+2)

By given data:

(x) + (x +2) = 48

2 x + 2 = 48

2 x = 48 -2

2 x = 46

x = 23

The numbers are 23 and 25

The two odd consecutive integers are 23 and 25.

A consecutive integer defines the continuous integers with difference of 1. That is, consecutive integers are x, x + 1, x + 2, x + 3, ... Every integer has a difference of 1 with their neighbor.

2, 3, 4, 5...

-5, -4, -3, -2, ...

Three consecutive numbers are one of the part in math. Numbers which follow each other in order, without spaces, from smallest to largest is known as consecutive numbers. For example 12, 13 and 14 are three consecutive numbers.Below you could see examples for three consecutive integers and sum of three consecutive integers.

Step 1: Let us assume the integers are x, x + 1 and x + 2 .

Step 2: And we know that , the least and greatest of the 3 consecutive integer is 160 .

Step 3: So, we can arrange the equation, that is x + (x + 2) = 160 .

Step 4: Here we need to solve this equation. So 2x + 2 = 160. (Subtract 2 on both the sides)

Step 5: Therefore x = 79. Therefore the least integer is 79.

Step 6: Substitute the x value is x + 1, x + 2 .

Step 7: Therefore, 79 + 1 = 80 and 79 + 2 = 81.

Step 8: Therefore , the values of 3 integers are 79, 80 and 81.

Step 1: Let us assume the integers are x, x + 1 and x + 2 .

Step 2: And we know that , the least and greatest of the 3 consecutive integer is 180 .

Step 3: So, we can arrange the equation, that is x + (x+2) = 180 .

Step 4: Here we need to solve this equation. So 2x + 2 = 180. (Subtract 2 on both the sides)

Step 5: Therefore x = 89. Therefore the least integer is 89.

Step 6: Substitute the x value is x+1, x+2 .

Step 7: Therefore, 89+1 = 90 and 89+2 = 91.

Step 8: Therefore , the values of 3 integers are 89, 90 and 91.

Consecutive integers = x+x+1+x+2 = 18

3x+3=18

Subtract both sides by 3 we get,

3x+3-3 = 18-3

3x = 15

Divide both sides by 3 we get,

$\frac{3x}{3}$ = $\frac{15}{3}$

X = 5

Therefore, the unknown number is 5.

Then, three consecutive integers are,

X = 5

X+1 = 6

X+2 = 7

Three Integers are 5, 6 and 7

Below you could see examples for two consecutive integers and sum of two consecutive integers

Let x be one of the consecutive numbers.

x + 1 is the other consecutive number

The sum of these two consecutive numbers is x+(x+1)= x+x+1= 2x+1

Given the sum is 15

Therefore 2x + 1 = 15

=> 2x = 15-1 = 14

=> 2x = 14

=> x = $\frac{14}{2}$ =7

=> x = 7

The consecutive number is x + 1 = 8

The two consecutive numbers are 7, 8.

Step 1: Write the given two consecutive even integer = 104.

Step 2: Let us assume the odd integer as ‘x’.

Step 3: Then the formula is given by ‘x’ is ‘x’ + 2.

Step 4: Simplifying the given expression, we get,

x + (x + 2) = 104

x + x + 2 = 104

2x + 2 = 104

2x = 104 – 2

2x = 102

Divide by 2 on both the sides

$\frac{2x}{2}$ = $\frac{102}{2}$

x = 51

The next consecutive odd integer for 51 is 51 + 2 = 53.

Therefore, the two consecutive odd integers for 167 is given by 51 and 53.

Let the first integer = n

Second integer = n+1

Sum of the two consecutive integers = 75

n+(n+1) = 75

2n+1 = 75

2n = 75-1

2n = 74

n = $\frac{74}{2}$

n = 37

n+1 = 37+1= 38

Hence, the two integers are 37, 38

Let, 1st integer = n

2nd = n + 1

3rd = n + 2

4th = n + 3

Large two integers are n + 2, n + 3

According to question:

(n + 2) + (n + 3) = 65

2n + 5 = 65

2n = 65 - 5

2n = 60

n = $\frac{60}{2}$

n = 30 (first integer)

Second integer = n + 1 = 30 + 1 = 31

Third integer = n + 2 = 30 + 2 = 32

and forth integer = n + 3 = 30 + 3 = 33

Hence four consecutive integers are, 30, 31, 32, 33.

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