Consecutive integers

Consecutive intergers article deals with the definition and it's types and the model problems related to it

Consecutive integers definition:

In algebra, the consecutive integers are the integers that follow in a sequence, that is each number begin 1 more than a previous number. It is represented by n, n+1, n+2..., where n is any integer.


Types of consecutive integers:

• Even consecutive integers
• Odd consecutive integers

Types of consecutive integers

• Even consecutive integers:

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

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

• Odd consecutive integers:

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

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


Examples


Here are some consecutive integers problems -

Problem 1:

Find three Consecutive Integers when their sum is 33.

Solution:

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

3v+3 = 33

3v = 33-3

3v = 30

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

v  = 10

The algebra consecutive integers are

v =10

v + 1= 11

v + 2 = 13

The consecutive integers are 10, 11, and 13.

Problem 2:

Find the algebra even three consecutive intergers where their sum is 66.

Solution:

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

3v + 6 = 66

3v = 66-6

3v = 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.

Problem 3:

Find the two odd consecutive integers whose sum is 48

Solution:

Sum of two odd consecutive integers are 48

Let the odd consecutive integers are x,x+2

By given data:

x + x +2 = 48

2x + 2 = 48

2x = 48 -2

2x = 46

x = 23

The numbers are 23 and 2

The two odd consecutive integers are 23 and 25.