# Sum of First n Natural Numbers

We will discuss here how to find the sum of first n natural numbers.

Let S be the required sum.

Therefore, S = 1 + 2 + 3 + 4 + 5 + .................... + n

Clearly, it is an Arithmetic Progression whose first term = 1, last term = n and number of terms = n.

Therefore, S = $$\frac{n}{2}$$(n + 1), [Using the formula S = $$\frac{n}{2}$$(a + l)]

Solved examples to find the sum of first n natural numbers

1. Find the sum of first 25 natural numbers.

Solution:

Let S be the required sum.

Therefore, S = 1 + 2 + 3 + 4 + 5 + .................... + 25

Clearly, it is an Arithmetic Progression whose first term = 1, last term = 25 and number of terms = 25.

Therefore, S = $$\frac{25}{2}$$(25 + 1), [Using the formula S = $$\frac{n}{2}$$(a + l)]

= $$\frac{25}{2}$$(26)

= 25 × 13

= 325

Therefore, the sum of first 25 natural numbers is 325.

2. Find the sum of first 100 natural numbers.

Solution:

Let S be the required sum.

Therefore, S = 1 + 2 + 3 + 4 + 5 + .................... + 100

Clearly, it is an Arithmetic Progression whose first term = 1, last term = 100 and number of terms = 100.

Therefore, S = $$\frac{100}{2}$$ (100 + 1), [Using the formula S = $$\frac{n}{2}$$(a + l)]

= 50(101)

= 5050

Therefore, the sum of first 100 natural numbers is 5050.

3. Find the sum of first 500 natural numbers.

Solution:

Let S be the required sum.

Therefore, S = 1 + 2 + 3 + 4 + 5 + .................... + 500

Clearly, it is an Arithmetic Progression whose first term = 1, last term = 500 and number of terms = 500.

Therefore, S = $$\frac{500}{2}$$(500 + 1), [Using the formula S = $$\frac{n}{2}$$(a + l)]

= 225(501)

= 112725

Therefore, the sum of first 100 natural numbers is 112725.

Arithmetic Progression

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Estimating Sum and Difference | Reasonable Estimate | Procedure | Math

May 22, 24 06:21 PM

The procedure of estimating sum and difference are in the following examples. Example 1: Estimate the sum 5290 + 17986 by estimating the numbers to their nearest (i) hundreds (ii) thousands.

2. ### Round off to Nearest 1000 |Rounding Numbers to Nearest Thousand| Rules

May 22, 24 06:14 PM

While rounding off to the nearest thousand, if the digit in the hundreds place is between 0 – 4 i.e., < 5, then the hundreds place is replaced by ‘0’. If the digit in the hundreds place is = to or > 5…

3. ### Round off to Nearest 100 | Rounding Numbers To Nearest Hundred | Rules

May 22, 24 05:17 PM

While rounding off to the nearest hundred, if the digit in the tens place is between 0 – 4 i.e. < 5, then the tens place is replaced by ‘0’. If the digit in the units place is equal to or >5, then the…

4. ### Round off to Nearest 10 |How To Round off to Nearest 10?|Rounding Rule

May 22, 24 03:49 PM

Round off to nearest 10 is discussed here. Rounding can be done for every place-value of number. To round off a number to the nearest tens, we round off to the nearest multiple of ten. A large number…

5. ### Rounding Numbers | How do you Round Numbers?|Nearest Hundred, Thousand

May 22, 24 02:33 PM

Rounding numbers is required when we deal with large numbers, for example, suppose the population of a district is 5834237, it is difficult to remember the seven digits and their order