Find 5 Consecutive Integers Whose Sum is 265 by 3 Ways

The sum of five consecutive integers is 265, what are these integers? Through the consecutive integers calculator, we can get the answer are 51, 52, 53, 54 and 55. You must be interested in how to find these 5 consecutive integers whose sum is 265. There are three methods here, let us introduce them one by one below.

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, the 5th integer is N + 4.

Therefore, the sum of 5 consecutive integers is 265, which can be expressed by the equation

N + (N + 1) + (N + 2) + (N + 3) + (N + 4) = 265

Solve this equation

N + (N + 1) + (N + 2) + (N + 3) + (N + 4) = 265
N + N + 1 + N + 2 + N + 3 + N + 4 = 265

5 * N + 1 + 2 + 3 + 4 = 265
5 * N + 10 = 265
5 * N = 265 – 10
5 * N = 255
N = 255 / 5
N = 51

Now, we can get that 51 is the first integer of 5 consecutive integers whose sum is 265. So, the second integer is 52, the third integer is 53, the 4th integer is 54, the 5th integer is 55.

The answer came out, the sum of 5 consecutive integers is 265, these five integers are 51, 52, 53, 54 and 55.

Verify: 51 + 52 + 53 + 54 + 55 = 265. Correct!

This is the most common method, let’s look at the second method, which is my favorite 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 five consecutive integers whose sum is 265. In here, M = 5, S = 265. Replace them in the formula to calculate the first integer

First(n) = 265 / 5 – (5 – 1) / 2 = 53 – 4 / 2 = 53 – 2 = 51

The first integer is 51, so, it can be easily calculated that the second integer is 52, the third integer is 53, the 4th integer is 54, the 5th integer is 55.

Thus, the answer are also 51, 52, 53, 54 and 55. Same as the first method. Then look at the third method, which is the simplest one.

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 5 consecutive integers is 265, so, the average of these 5 consecutive integers is 265 / 5 = 53. The integers around 53 are 49, 50, 51, 52, 53, 54, 55, 56, 57. Now the problem is simple, find 5 consecutive integers from 49 to 57 and their average is 53. The answer are 51, 52, 53, 54 and 55.

So the sum of 5 consecutive integers is 265, these integers are 51, 52, 53, 54, 55. The results are consistent with the above two methods. Is it very simple?

Now, we have found out these 5 consecutive integers whose sum is 265, some problems can be easily solved.

On this page, In addition to introducing three methods how to find five consecutive integers whose sum is 265, it also provides a calculator that calculates five 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 5, or you need to calculate consecutive odd integers or even integers. You can use our other more advanced Consecutive 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.