Find your Math Personality!

Find your Math Personality!

# 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

**☛ Related Questions:**

- A contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day, etc., the penalty for each succeeding day being Rs. 50 more than for the preceding day. How much money the contractor has to pay as penalty if he has delayed the work by 30 days?
- A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
- In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?
- A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, . . .as shown in Fig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles? [Take π = 22/7]

Math worksheets and

visual curriculum

visual curriculum