Sum of First N Numbers Calculator - Natural, Even, Odd, Prime & Composite

Welcome to the sum of first N numbers calculator, where the following 5 problems can be easily solved:

Natural numbers refer to the set of non-negative integers, i.e. 0 and positive integers, which are often represented by N. To calculate the sum of first N natural numbers, you must find out first N natural numbers first, and then add up these natural numbers to get the answer.

For example, the sum of first 6 natural numbers.

1. First 6 natural numbers are: 0, 1, 2, 3, 4, 5
2. The sum of first 6 natural numbers is: 0 + 1 + 2 + 3 + 4 + 5 = 15

Calculate the sum of first N natural numbers using the formula

From the definition of natural numbers above, we know that natural numbers are a set of arithmetic sequences, the first item is 0, and the tolerance is 1. According to the formula of the sum of first N items of arithmetic sequence

S_n = n * a₁ + n * (n – 1) * d2

Among them, a₁ is the first item of the sequence, d is the tolerance.

The formula of the sum of first N natural numbers can be derived as follows:

S_n = n * a₁ + n * (n – 1) * d2

= n * 0 + n * (n – 1) * 12

= n * (n – 1)2

For example, the sum of first 6 natural numbers above, use the formula to calculate:

6 * (6 – 1) 2 = 6 * 52 = 15

It is consistent with the calculation result above.

A number that can be divided by 2 is called an even number. Note that, the quotient of 0 divided by 2 is also 0, so 0 is also classified as an even number. To calculate the sum of first N even numbers, first, find out first N even numbers; then add up these even numbers to get the desired result.

For example, the sum of first 6 even numbers.

1. First 6 even numbers are: 0, 2, 4, 6, 8, 10
2. The sum of first 6 even numbers is: 0 + 2 + 4 + 6 + 8 + 10 = 30

Calculate the sum of first N even numbers using the formula

Obviously, even numbers are also a set of arithmetic sequences, the first item is 0, and the tolerance is 2. According to the formula of the sum of first N items of arithmetic sequence

S_n = n * a₁ + n * (n – 1) * d2

Among them, a₁ is the first item of the sequence, d is the tolerance.

The formula of the sum of first N even numbers can be derived as follows:

S_n = n * a₁ + n * (n – 1) * d2

= n * 0 + n * (n – 1) * 22

= n * (n – 1)

So, the sum of first 6 even numbers can be calculated by the formula:

6 * (6 – 1) = 6 * 5 = 30

It is consistent with the calculation result above.

In integers, numbers that cannot be divided by 2 are called odd numbers. Similarly, to calculate the sum of first N odd numbers, you must find out first N odd numbers first; then add up these odd numbers to get the sum result.

For example, the sum of first 6 odd numbers.

1. First 6 odd numbers are: 1, 3, 5, 7, 9, 11
2. The sum of first 6 odd numbers is: 1 + 3 + 5 + 7 + 9 + 11 = 36

Calculate the sum of first N odd numbers using the formula

Like even numbers, odd numbers are also a set of arithmetic sequences, the first item is 1, and the tolerance is 2. According to the formula of the sum of first N items of arithmetic sequence

S_n = n * a₁ + n * (n – 1) * d2

Among them, a₁ is the first item of the sequence, d is the tolerance.

The formula of the sum of first N odd numbers can be derived as follows:

S_n = n * a₁ + n * (n – 1) * d2

= n * 1 + n * (n – 1) * 22

= n²

So, the sum of first 6 odd numbers can be calculated by the formula:

6² = 36

It is consistent with the calculation result above.

A prime number is an integer that has no factors other than 1 and itself among the natural numbers greater than 1. To calculate the sum of first N prime numbers, first, find out first N prime numbers; then, add up these prime numbers to get the result.

For example, the sum of first 6 prime numbers.

1. First 6 prime numbers are: 2, 3, 5, 7, 11, 13
2. The sum of first 5 prime numbers is: 2 + 3 + 5 + 7 + 11 + 13 = 41

A composite number is an integer greater than 1 that is divisible by other integers in addition to 1 and itself. To calculate the sum of first N composite numbers, first, find out first N composite numbers; then, add them together.

For example, the sum of first 6 composite numbers.

1. First 6 composite numbers are: 4, 6, 8, 9, 10, 12
2. The sum of first 5 composite numbers is: 4 + 6 + 8 + 9 + 10 + 12 = 49

The procedure to use the sum of first N numbers calculator is as follows: