Consecutive even Integers

Introduction to even integers:

The integers are formed by the natural numbers including 0 (0, 1, 2, 3 ...) along with the negative of the non-zero natural numbers (−1, −2, −3 ...). Integers are viewed as subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set ... −2, −1, 0, 1, 2 .... For example, 65, 7, and −756 are integers; 1.6 and 1½ are not integers. The set of all integers is denoted by a boldface Z, which stands for Zahlen. In this article we shall discus about even integers

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Sample for even Integers:

Any integer which can be divided exactly by 2.
The last digit  of even integers will be 0, 2, 4, 6 or 8
Ex: -24, 0, 6 and 38 are all even integers
Sample of an Integer:

A number has no fractional part.
Includes the counting numbers like {1, 2, 3…}, zero {0}, and the negative of the counting numbers {-1, -2, -3 …}
You can write them down like this: {…, -3, -2, -1, 0, 1, 2, 3 …}

Rules of even Integers:
Integers are whole numbers, for example, –4, –3, –2, –1, 0, 1, 2, 3, 4...

Optimistic integers are the whole numbers greater than zero, i.e.: 1, 2, 3, 4, 5... We say that its sign is positive. Negative integers are the whole numbers less than zero, i.e.: –1, –2, –3, –4, –5... We say that its sign is negative.
Consecutive integers are integers which  follow in sequence, every number being 1 more than the before number, represented by n, n +1, n + 2, n + 3.... Where n is any integer. For ex: 23, 24, 25 …
If we begin with an even number , the consecutive number is 2 more than the previous number in the sequence, then we will get consecutive even integers.


Even Integers

An even integer n is any integer which is a multiple of 2.
Every even integer can be written in the form 2k for some unique integer k.
The even integers with smallest absolute value are 0, 2, -2, 4, and 4.
The sum and variation of any  two even integers is even, and the product of any two even integers is not only even but is also   divisible by 4.
The sum of an even and an odd integer is odd.
While all even integers are divisible by 2, 2 is the only prime even integer.

Examples Based on Consecutive even Integers:

Ex: 1 Addition of two consecutive even integers is 178.What is the two integers?

Sol:

Given the addition of two consecutive even integer = 178.

Let an even integer is ‘y’.

Next even integer to this ‘y’ is ‘y + 2’.

y + (y + 2) = 178

y + y + 2 = 178

2y + 2 = 178

2y = 178 – 2

2y = 176  

y = 88

A next consecutive even integer to 88 is 88 + 2 = 90.

The two consecutive even integers whose addition is 178 are 88 and 90.

Ex: 2 Addition of two consecutive even integers is -102. What is the two integers?

Sol:

Given addition of two consecutive even integers = -102

y + (y + 2) = -102

y + y + 2 = -102

2y = - 102 – 2

2y = -104

Y = -52

Next even integer to -52 is -52 + 2 = -50

Therefore the two consecutive even integers are -52 and -50 gives the addition of -102.

Practice problems on consecutive even integers:

Pro: 1 Addition of two consecutive even integers is -14. What is the two integers?

Ans: -8 and -6.

Pro: 2 Addition of two consecutive even integers is 74. What is the two integers?

Ans: 36 and 38.