# Find the sum of the odd numbers between 0 and 50

**Solution:**

The sum of the first n terms of an AP is given by S_{n} = n/2 [2a + (n - 1) d] or S_{n} = n/2 [a + l].

Here, a is the first term, d is a common difference and n is the number of terms.

The odd numbers between 0 and 50 are 1, 3, 5, 7, 9 ... 49

Therefore, it can be observed that these odd numbers are in an A.P.

Hence,

- First term, a = 1
- Common difference, d = 2
- Last term, l = 1

We know that nth term of AP, a_{n} = l = a + (n - 1)d

49 = 1 + (n - 1) 2

48 = 2(n - 1)

n - 1 = 24

n = 25

We know that sum of n terms of AP,

S_{n} = n/2 [a + l]

S_{25} = 25/2 (1 + 49)

= 25/2 × 50

= 25 × 25

= 625

**Video Solution:**

## Find the sum of the odd numbers between 0 and 50

### Class 10 Maths NCERT Solutions - Chapter 5 Exercise 5.3 Question 14 :

Find the sum of the odd numbers between 0 and 50

The sum of the odd numbers between 0 and 50 is 625