Consecutive Even Numbers with Examples and FAQs

What are consecutive even numbers?

Before discussing consecutive even numbers first let’s start by knowing about consecutive numbers.

Consecutive numbers

Numbers that follow a regular sequence or pattern are called consecutive numbers. It’s a series where the difference between the numbers is fixed. The series starts from the smallest number and tends towards the largest number. For example, the set of natural numbers from 1 to 10, i.e., 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, is a list of consecutive numbers where the fixed difference is ‘1’ between each number.

Consecutive Even Numbers

Even numbers are numbers that end in either 0, 2, 4, 6 or 8. A set of even consecutive numbers is such a set where the difference between each consecutive number is ‘2’. This list can be represented in the form p, p + 2, p + 4, p + 6, p + 8, … and so on. Here, p is the starting number which can be either an even integer or an even natural number.

Properties of Even Consecutive Numbers

In general, consecutive numbers follow a pattern, where the series starts from the smallest number and continues till the largest.

Following are some properties of consecutive numbers that are even:

• The difference between each number of the series is fixed, and it is 2 in the case of even consecutive numbers.
• The numbers in the list can only end in 0, 2, 4, 6 and 8.
• The sum of all the consecutive numbers is also an even number.

Examples

Examples 1: Does the given sequence follow the properties of consecutive numbers that are even?

Solution: 

In the given sequence all numbers are even and the difference between each element of the series from the beginning to the end is ‘2’. Hence, the given sequence is that of consecutive evens.

Example 2: The sum of 5 even consecutive numbers is 100. Can you identify the numbers using the concept of consecutive evens?

Solution:

Let the first element of the series of 5 consecutive evens be ‘a’. Then the series is:

a, (a + 2), (a + 4), (a + 6), ( a + 8).

It is given that the sum of 5 consecutive elements is 100.

\therefore a+(a+2)+(a+4)+(a+6)+(a+8)=100
\Rightarrow(a+a+a+a+a)+(2+4+6+8)=100
\Rightarrow 5 a+20=100
\Rightarrow 5 a=100-20=80
\therefore a=\frac{80}{5}=16

Hence, the numbers are:

16,(16+2),(16+4),(16+6),(16+8) \Rightarrow 16,18,20,22,24.