How can You Find the Sum of the First 100 Natural Numbers?

A natural number is one that frequently appears in maths and is used to calculate or simplify expressions with the help of mathematical operators. It is, therefore, the same as the set of whole numbers except for the term 0, and the set represents all the non-negative and nonfractional numbers. There is an approach to defining the collection of natural numbers N: N = (1, 2, 3, 4,…}. Now that you know about natural numbers so in this article let’s look at how can you find the sum of the first 100 natural numbers, what is the average of the first 100 natural odd numbers, and what is the mean of first 100 natural numbers.

1. How do you Find the Sum of Natural Numbers?

Using the arithmetic succession formula, which assumes a common difference of 1 between the preceding and next numbers. The summation of natural numbers can be calculated. Natural numbers, which include 1, 2, 3, 4, 5, 6, and so on, are known as counting numbers since they range from 1 to infinity. 

To calculate the sum of n natural numbers or to find the sum of the first 100 natural numbers, use this formula,

S = n(n + 1)/2. (See Prime and Composite numbers)

2. What is the First 100 Natural Numbers?

First 100 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 and 100. (See How to Write 1 Million in Numbers?) 

3. How can you Find the Sum of the First 100 Natural Numbers?

To find the sum of the first 100 natural numbers you can use the formula given below:

S = n/2 [2a + (n − 1) × d], where a is the first term, n is the number of natural numbers from 1 to 100, and d is the difference between two consecutive terms.

You can also use this sum formula to get the value, S = n(n + 1)/2, where S is the sum and n represents the number i.e. 100.

Anyway, who found the sum of first 100 natural numbers? Let’s look at it in the next question. (See What is the Very Last Number in the World?)

4. Who Found the Sum of First 100 Natural Numbers?

The discovery of the first 100 natural numbers’ sum is credited to Gauss, a well-known mathematician. When Gauss was a little lad, he was tasked with adding numbers from 1 to 100. (See When Were Numbers invented?) 

5. How do you Find the Sum of the First 100 Odd Numbers?

As above we have already discussed how to find the sum of the first 100 natural numbers. Now, you can use the given formula to find the sum of the first 100 odd numbers

Sum of first 100 odd numbers = n/2 {2a + (n − 1) d},

where a is the first term, n is the number of terms remaining till the nth term. d is a common difference, which must be 2 in this case. Must read What are the Factors of 80?

6. How do you Find the Sum of the First 100 Natural Numbers in Excel?

The following steps will help you to find the sum of the first 100 natural numbers in Excel:

• In Microsoft Excel, the AutoSum tool allows you to sum whole columns or rows.
• Although the AutoSum tool chooses a column or row of values mechanically, you can choose any number combination by dragging and clicking with the mouse.
• In Excel, you may manually add a group of integers by entering the SUM function.
• By tapping the sum cell and glancing at the formula bar just at the top of the display, you can see the specifics of your computation.

7. What is the Mean of First 100 Natural Numbers?

The arithmetic mean is the average value within a given set of data. The arithmetic mean is thus obtained by adding the sum of all values divided by the total number of values.

Arithmetical mean = (1 + 2 + 3 + 4 +….+ 100) /100,

= 5050/100,

= 50.5

Moreover, you could also use the Arithmetical mean = n(n + 1)/2n, to get the mean. (See How to find the Common Difference of the Arithmetic Sequence?)

8. What is the Sum of the First 100 Prime Numbers?

Prime numbers are those that are bigger than 1. Only the digit itself and 1 are the factors of those numbers. This indicates that no value besides 1 and the value itself may be used to divide these values without providing a residue. So, the sum of the first 100 prime numbers is (2 + 3 +….+ 97+101+…+523+541) which is equal to 24133. (See What Do You Mean By Prime Number?)

9. What are the First 100 Odd Numbers?

The first 100 odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99. 

10. What is the Average of the First 100 Natural Odd Numbers?

The average is calculated by adding all the numbers divided by the total count of odd numbers. So, the average of the first 100 natural odd numbers is

(1 + 3 + 5 +….99)/50 = 50. (See How Calculator Works?)

11. How do you Find the Sum of n Odd Natural Numbers?

Since the common difference of odd numbers is 2, the sequence of odd numbers, therefore, constitutes an arithmetic progression. We can find the sum of the first n (i.e., sequence starts with 1) odd natural numbers by using this formula, which is the sum of n odd numbers = n², where the term count is indicated by the natural integer n. (See Why is Mathematical Concept Important?)