Question

The sum of \[4\] consecutive integers is \[178\]. What are those integers?

Answer 1

Hint: We can assume our \[4\] consecutive integers are \[a - 1,{\text{ }}a,{\text{ }}a + 1,{\text{ }}a + 2\]. Integers can be both positive and negative, including zero. In a set of consecutive integers (or in numbers), the mean and median are equal. All properties and identities for addition, subtraction, multiplication and division of numbers are also applicable to all the integers.

Complete step-by-step solution:
We assume our \[4\] consecutive numbers as $(a-1), a, (a+1), (a+2).$
We will find the sum of 4 consecutive numbers,
\[ = \left( {a - 1} \right) + a + \left( {a + 1} \right) + \left( {a + 2} \right)\]
\[ = 4a + 2\]
Given, The sum of \[4\] consecutive integers is 178,
We will equate the values to find the value of a,
\[4a + 2 = 178\]
\[\Rightarrow 4a = 178 - 2\]
\[\Rightarrow a = 44\]
we will put the value of a, and find the integers
\[a - 1 = 44 - 1 = 43\]
\[\Rightarrow a = 44\]
\[\Rightarrow a = 44 + 1 = 45\]
\[\Rightarrow a + 2 = 44 + 2 = 46\]
So, our consecutive integers are 43,44,45,46.

Note: We may be asked in some questions that the product of \[4\] number is something, and the difference between each number is assumed to be $2$ ,
if there are \[4\] numbers we should assume: \[x - 3,{\text{ }}x - 1,{\text{ }}x + 1,{\text{ }}x + 3\].
If there are \[3\] numbers, we should assume: \[x - 2,{\text{ }}x,{\text{ }}x + 2\].
Because when we multiply them, they will form squares. And on top of that, we only have x.
The formula to get a consecutive integer is \[{{n}}{\text{ }} + {\text{ }}{{1}}\]. the general form of a consecutive odd integer is \[{{2n}} + {{1}}\]
The general form of a consecutive even integer is \[{{2n}}\] , where n is an integer.