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**

**Definition of Arithmetic Progression****General Form of an Arithmetic Progress****Arithmetic Mean****Sum of the First n Terms of an Arithmetic Progression****Sum of the Cubes of First n Natural Numbers****Sum of First n Natural Numbers****Sum of the Squares of First n Natural Numbers****Properties of Arithmetic Progression****Selection of Terms in an Arithmetic Progression****Arithmetic Progression Formulae****Problems on Arithmetic Progression****Problems on Sum of 'n' Terms of Arithmetic Progression**

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