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 Sₙ = n/2 [2a + (n - 1) d] or Sₙ = 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 lying 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, aₙ = 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,

Sₙ = n/2 [a + l]

S₂₅ = 25/2 (1 + 49)

= 25/2 × 50

= 25 × 25

= 625

☛ Check: NCERT Solutions Class 10 Maths Chapter 5

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

Summary:

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

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