Solved Examples on Sum of Odd Numbers

Example 1: Find the sum of the first 7 odd numbers.

Solution:

Given: n is the number of terms in the series = 7,

a is the first odd number = 1, and

d is the common difference = 2

Now, substitute the values into the formula: S_n = n/2×(2a+(n−1)d)

S_n = 7/2 × [2×1 + (7−1)×2]

⇒ S_n = 7/2 × [2+12]

⇒ S_n = 7/2 × 14

⇒ S_n = 49

Therefore, the sum of the first 7 odd numbers is 49.

Example 2: Find the sum of odd numbers between 1 to 20.

Solution:

The odd numbers between 1 and 30 are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Sum of Odd numbers = 1 + 3+ 5 + 7 + 9 + 11 + 13+ 15 + 17 + 19 = 100

Hence, the sum of odd numbers between 1 to 20 is 100.

Example 3: Seema has 5 Pencils. He bought 3 more Pencils. How many Pencils does Seema have?

Solution:

Seema has 5 pencils.

He bought 3 more pencils.

Total Pencil = 5 + 3 pencils

Thus, Total Pencil = 8 pencils

So, the total number of pencils = 8

Example 4: Find the sum of odd numbers between 1 to 30.

Solution:

The odd numbers between 1 and 30 are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29.

Sum of Odd numbers = 1 + 3+ 5 + 7 + 9 + 11 + 13+ 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 = 225.

Hence, the sum of odd numbers between 1 to 30 is 225.

Example 5: Add any two Consecutive Odd numbers, You will get even number. Justify this statement.

Solution:

Let’s take two odd numbers = 3,5

Add both the numbers = 3 + 5

= 8

Hence, 8 is an even number because it is divisible by 2.

Therefore, the above statement is also justified, the addition of two consecutive numbers will give an even number.

Example 6: Find the sum of the first 5 odd numbers using the formula S_n= 1/2×n(2a+(n−1)d).

Solution:

So, here the sum in arithmetic series is given as S_n= 1/2×n(2a+(n−1)d).

Given: n is the number of terms in the series = 5,

a is the first odd number = 1, and

d is the common difference = 2

Now, substitute the values into the formula:

S₅ = 5/2 × [2×1 + (5−1)×2]

⇒ S₅ = 5/2 × [2+8]

⇒ S₅ = 5/2 × 10

⇒ S₅ = 25

Therefore, the sum of the first 5 odd numbers is 25.

Sum of Odd Numbers is calculated by adding together integers that are not divisible by 2, resulting in a total that is either an odd number or even number. Sum of Odd Numbers is often represented by the formula expressed as n² where n is a natural number. This formula can be used to calculate the sum of the first n odd numbers without adding them individually.

In this article, we will learn about the Sum of Odd Number Formula including the definition of Odd Numbers as well as some solved examples using the formula.