Find 6 Consecutive Even Integers Whose Sum is 270 by 3 Ways

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The sum of six consecutive even integers is 270, what are these even integers? I can easily tell you that the answer are 40, 42, 44, 46, 48 and 50. You must be interested in how to find these 6 consecutive even integers whose sum is 270. There are three methods here, let us introduce them one by one below.

1. Find six consecutive even integers whose sum is 270 by 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, the 4th even integer is 2 * N + 6, the 5th even integer is 2 * N + 8, the 6th even integer is 2 * N + 10.

Therefore, the sum of 6 consecutive even integers is 270, which can be expressed by the equation

2 * N + (2 * N + 2) + (2 * N + 4) + (2 * N + 6) + (2 * N + 8) + (2 * N + 10) = 270

Solve this equation

2 * N + (2 * N + 2) + (2 * N + 4) + (2 * N + 6) + (2 * N + 8) + (2 * N + 10) = 270

2 * N + 2 * N + 2 + 2 * N + 4 + 2 * N + 6 + 2 * N + 8 + 2 * N + 10 = 270

12 * N + 2 + 4 + 6 + 8 + 10 = 270

12 * N + 30 = 270

12 * N = 270 – 30

12 * N = 240

N = 240 / 12

N = 20

So, 2 * N = 2 * 20 = 40

Now, we can get that 40 is the first integer of 6 consecutive even integers whose sum is 270. So, the second even integer is 42, the third even integer is 44, the 4th even integer is 46, the 5th even integer is 48, the 6th even integer is 50.

The answer came out, the sum of 6 consecutive even integers is 270, these three even integers are 40, 42, 44, 46, 48 and 50.

Verify: 40 + 42 + 44 + 46 + 48 + 50 = 270. Correct!

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

2. Find six consecutive even integers whose sum is 270 by 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 six consecutive even integers whose sum is 270. In here, M = 6, S = 270. Replace them in the formula to calculate the first even integer

First(e) = 270 / 6 – 6 + 1 = 45 – 6 + 1 = 40

The first even integer is 40, so, it can be easily calculated that the second even integer is 42, the third even integer is 44, the 4th even integer is 46, the 5th even integer is 48, the 6th even integer is 50.

Thus, the answer are also 40, 42, 44, 46, 48 and 50. Same as the first method. Then look at the third method, which is the simplest one.

3. Find six consecutive even integers whose sum is 270 by 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 6 consecutive even integers is 270, so, the average of these 6 consecutive even integers is 270 / 6 = 45. The even integers around 45 are 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53. Now the problem is simple, find 6 consecutive even integers from 37 to 53 and their average is 45. The answer are 40, 42, 44, 46, 48 and 50.

So the sum of 6 consecutive even integers is 270, these even integers are 40, 42, 44, 46, 48, 50. 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 6 consecutive even integers whose sum is 270, some problems can be easily solved.

  • The sum of six consecutive even integers is 270, the smallest one is 40.
  • 50 is the greatest even number of six consecutive even integers whose sum is 270.
  • The sum of six consecutive even integers is 270, the average of these even integers is 45.
  • The sum of six consecutive even integers is 270, the product of them is 40 * 42 * 44 * 46 * 48 * 50 = -429166592.
  • The sum of six consecutive even integers is 270, the sum of their squares is 402 + 422 + 442 + 462 + 482 + 502 = 12220.

Summarize

On this page, In addition to introducing three methods how to find six consecutive even integers whose sum is 270, it also provides a calculator that calculates six 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 6, 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 six consecutive even integers whose sum is 270. 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?

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