# Find Four Consecutive Integers Whose Sum is 138 by 3 Ways

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The sum of four consecutive integers is 138, what are these integers? I can easily tell you that the answer are 33, 34, 35 and 36. You must be interested in how to find these 4 consecutive integers whose sum is 138. There are three methods here, let us introduce them one by one below.

## How to find four consecutive integers whose sum is 138?

### 1. 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, the 4th integer is N + 3.

Therefore, the sum of 4 consecutive integers is 138, which can be expressed by the equation

N + (N + 1) + (N + 2) + (N + 3) = 138

Solve this equation

N + (N + 1) + (N + 2) + (N + 3) = 138

N + N + 1 + N + 2 + N + 3 = 138

4 * N + 6 = 138

4 * N = 138 – 6

4 * N = 132

N = 132 / 4

N = 33

Now, we can get that 33 is the first integer of 4 consecutive integers whose sum is 138. So, the second integer is 34, the third integer is 35, the 4th integer is 36.

The answer came out, the sum of 4 consecutive integers is 138, these three integers are 33, 34, 35 and 36.

Verify: 33 + 34 + 35 + 36 = 138. Correct!

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

### 2. 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 four consecutive integers whose sum is 138. In here, M = 4, S = 138. Replace them in the formula to calculate the first integer

First(n) = 138 / 4 – (4 – 1) / 2 = 34.5 – 3 / 2 = 34.5 – 1.5 = 33

The first integer is 33, so, it can be easily calculated that the second integer is 34, the third integer is 35, the 4th integer is 36.

Thus, the answer are also 33, 34, 35 and 36. Same as the first method. Then look at the third method, which is the simplest one.

### 3. 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 4 consecutive integers is 138, so, the average of these 4 consecutive integers is 138 / 4 = 34.5. The integers around 34.5 are 32, 33, 34, 35, 36, 37, 38. Now the problem is simple, find 4 consecutive integers from 32 to 38 and their average is 34.5. The answer are 33, 34, 35 and 36.

So the sum of 4 consecutive integers is 138, these integers are 33, 34, 35, 36. 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 4 consecutive integers whose sum is 138, some problems can be easily solved.

• 1. What are four consecutive integers whose sum is 138?
The answer are 33, 34, 35 and 36.
• 2. What is the smallest of four consecutive integers whose sum is 138?
The smallest number is 33.
• 3. What is the greatest of four consecutive integers whose sum is 138?
The greatest number is 36.
• 4. What is the average of four consecutive integers whose sum is 138?
The average of these 4 consecutive integers is (33 + 34 + 35 + 36) / 4 = 138 / 4 = 34.5.
• 5. What is the product of four consecutive integers whose sum is 138?
The sum of 4 consecutive integers is 138, the product of them is 33 * 34 * 35 * 36 = 1413720.
• 6. What is the sum of square of four consecutive integers whose sum is 138?
The sum of 4 consecutive integers is 138, the sum of their squares is 332 + 342 + 352 + 362 = 4766.

## Summarize

On this page, In addition to introducing three methods how to find four consecutive integers whose sum is 138, it also provides a calculator that calculates four 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 4, 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 four consecutive integers whose sum is 138. Personally, I prefer the second method, 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?