# Find Three Consecutive Integers Whose Sum is 126 by 3 Ways

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The sum of three consecutive integers is 126, what the integers? I can easily tell you that the answer are 41, 42 and 43. You must be interested in how to find these 3 consecutive integers whose sum is 126. There are three methods here, let us introduce them one by one below.

## 1. Find three consecutive integers whose sum is 126 by hypothetical method

Assuming that N is used to represent the first integer, so the second integer is N + 1, the third integer is N + 2.

Therefore, the sum of 3 consecutive integers is 126, which can be expressed by the equation

N + (N + 1) + (N + 2) = 126

Solve this equation

N + (N + 1) + (N + 2) = 126

N + N + 1 + N + 2 = 126

3 * N + 3 = 126

3 * N = 126 – 3

3 * N = 123

N = 123 / 3

N = 41

Now, we can get that 41 is the first integer of 3 consecutive integers whose sum is 126. So, the second integer is 42, the third integer is 43.

The answer came out, the sum of 3 consecutive integers is 126, these three integers are 41, 42 and 43.

Verify: 41 + 42 + 43 = 126. Correct!

This is the most common method, let’s look at the second method, which is my favorite method.

## 2. Find three consecutive integers whose sum is 126 by formula method

According to the consecutive integers calculator based on sum, we can know that the sum of M consecutive integers is S, the first integer formula is

First(n) = S / M – (M – 1) / 2

M represents the number of consecutive integers.

S stands for sum.

Back to the problem we want to solve: find three consecutive integers whose sum is 126. In here, M = 3, S = 126. Replace them in the formula to calculate the first integer

First(n) = 126 / 3 – (3 – 1) / 2 = 42 – (3 – 1) / 2 = 42 – 1 = 41

The first integer is 41, so, it can be easily calculated that the second integer is 42, the third integer is 43.

Thus, the answer are also 41, 42 and 43. Same as the first method. Then look at the third method, which is the simplest one.

## 3. Find three consecutive integers whose sum is 126 by average method

The principle is very simple, because we want to calculate the consecutive integers, so after calculating the average, we can find the integers near the average.

The sum of 3 consecutive integers is 126, so, the average of these 3 consecutive integers is 126 / 3 = 42. The integers around 42 are 40, 41, 42, 43, 44, 45. Now the problem is simple, find 3 consecutive integers from 40 to 45 and their average is 42. The answer are 41, 42 and 43.

So the sum of 3 consecutive integers is 126, these integers are 41, 42, 43. The results are consistent with the above two methods. Is it very simple?

## Problems can be sloved by this answer

Now, we have found out these 3 consecutive integers whose sum is 126, some problems can be easily solved.

• The sum of three consecutive integers is 126, the smallest one is 41.
• The sum of three consecutive integers is 126, the middle integer is 42.
• The sum of three consecutive integers is 126, the greatest number is 43.
• The sum of three consecutive integers is 126, the average of these integers is 42.
• The sum of three consecutive integers is 126, the product of them is 41 * 42 * 43 = 74046.
• The sum of three consecutive integers is 126, the sum of their squares is 412 + 422 + 432 = 5294.

## Summarize

On this page, In addition to introducing three methods how to find three consecutive integers whose sum is 126, it also provides a calculator that calculates three consecutive integers based on the sum. If you encounter a similar problem next time, you can directly use this calculator to calculate the answer, which is very convenient.

Of course, if the problem you encounter is more complicated, such as: the number of consecutive integers is not 3, or you need to calculate consecutive odd integers or even integers. You can use our other more advanced sum-based consecutive integers calculator, where you can specify the number of consecutive integers and select consecutive integers type: natural integers, odd integers or even integers. I believe it can help you.

Well, that’s it, the above are three solutions to find three consecutive integers whose sum is 126. It’s not very complicated, but I personally like the second method best, because it can accurately calculate the first integer and the calculation process is very simple. So how about you? Please leave a message and tell me which method you like?