# Find Three Consecutive Even Integers Whose Sum is 42 by 3 Ways

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The sum of three consecutive even integers is 42, what are these even integers? I can easily tell you that the answer are 12, 14 and 16. You must be interested in how to find these 3 consecutive even integers whose sum is 42. There are three methods here, let us introduce them one by one below.

## How to find three consecutive even integers whose sum is 42?

### 1. Hypothetical method

Assuming that 2 * N is used to represent the first even integer, so the second even integer is 2 * N + 2, the third even integer is 2 * N + 4.

Therefore, the sum of 3 consecutive even integers is 42, which can be expressed by the equation

2 * N + (2 * N + 2) + (2 * N + 4) = 42

Solve this equation

2 * N + (2 * N + 2) + (2 * N + 4) = 42

2 * N + 2 * N + 2 + 2 * N + 4 = 42

6 * N + 2 + 4 = 42

6 * N + 6 = 42

6 * N = 42 – 6

6 * N = 36

N = 36 / 6

N = 6

So, 2 * N = 2 * 6 = 12

Now, we can get that 12 is the first integer of 3 consecutive even integers whose sum is 42. So, the second even integer is 14, the third even integer is 16.

The answer came out, the sum of 3 consecutive even integers is 42, these three even integers are 12, 14 and 16.

Verify: 12 + 14 + 16 = 42. 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 even integers is S, the first even integer formula is

First(e) = S / M – M + 1

M represents the number of consecutive even integers.

S stands for sum.

Back to the problem we want to solve: find three consecutive even integers whose sum is 42. In here, M = 3, S = 42. Replace them in the formula to calculate the first even integer

First(e) = 42 / 3 – 3 + 1 = 14 – 3 + 1 = 12

The first even integer is 12, so, it can be easily calculated that the second even integer is 14, the third even integer is 16.

Thus, the answer are also 12, 14 and 16. 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 even integers, so after calculating the average, we can find the even integers near the average.

The sum of 3 consecutive even integers is 42, so, the average of these 3 consecutive even integers is 42 / 3 = 14. The even integers around 14 are 10, 11, 12, 13, 14, 15, 16, 17, 18. Now the problem is simple, find 3 consecutive even integers from 10 to 18 and their average is 14. The answer are 12, 14 and 16.

So the sum of 3 consecutive even integers is 42, these even integers are 12, 14, 16. 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 even integers whose sum is 42, some problems can be easily solved.

• 1. What are three consecutive even integers whose sum is 42?
The answer are 12, 14 and 16.
• 2. What is the smallest of three consecutive even integers whose sum is 42?
The smallest number is 12.
• 3. What is the middle of three consecutive even integers whose sum is 42?
The middle integer is 14.
• 4. What is the greatest of three consecutive even integers whose sum is 42?
The greatest number is 16.
• 5. What is the average of three consecutive even integers whose sum is 42?
The average of these 3 consecutive even integers is (12 + 14 + 16) / 3 = 42 / 3 = 14.
• 6. What is the product of three consecutive even integers whose sum is 42?
The sum of 3 consecutive even integers is 42, the product of them is 12 * 14 * 16 = 2688.
• 7. What is the sum of square of three consecutive even integers whose sum is 42?
The sum of 3 consecutive even integers is 42, the sum of their squares is 122 + 142 + 162 = 596.

## Summarize

On this page, In addition to introducing three methods how to find three consecutive even integers whose sum is 42, it also provides a calculator that calculates three consecutive even 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 integers or consecutive odd 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 even integers whose sum is 42. 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?