# 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. ### Rupees and Paise | Paise Coins | Rupee Coins | Rupee Notes

Dec 04, 23 02:14 PM

Money consists of rupees and paise; we require money to purchase things. 100 paise make one rupee. List of paise and rupees in the shape of coins and notes:

2. ### Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

Dec 04, 23 01:50 PM

There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…