Finding Consecutive Integers: A step-by-step guide with an example problem and formula

Consecutive Integers

Consecutive integers are integers that follow each other in order, with a difference of 1 between each pair of consecutive integers

Consecutive integers are integers that follow each other in order, with a difference of 1 between each pair of consecutive integers. For example, the consecutive integers from 1 to 5 are 1, 2, 3, 4, 5.

To find consecutive integers, you can use the formula:

x, x+1, x+2, x+3, …

Where x is the starting integer and subsequent integers are obtained by adding 1 to the previous integer.

Here’s an example problem to illustrate how to find consecutive integers:

Find three consecutive integers such that the sum of the first and the third integers is 37.

Let’s assume the first consecutive integer is x. So, the second integer would be x + 1, and the third integer would be x + 2.

According to the problem, the sum of the first and the third integers is 37. So we can write the equation:

x + (x + 2) = 37

Simplifying the equation, we have:

2x + 2 = 37
2x = 37 – 2
2x = 35
x = 35/2
x = 17.5

Since we are looking for integer solutions, we need to discard the decimal value. Therefore, we can conclude that the first consecutive integer is 17.

Now, we can find the three consecutive integers by substituting the value of x:

First integer: x = 17
Second integer: x + 1 = 17 + 1 = 18
Third integer: x + 2 = 17 + 2 = 19

So, the three consecutive integers such that the sum of the first and the third integers is 37 are 17, 18, and 19.

I hope this example helps you understand how to find consecutive integers. Let me know if you have any further questions!

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