Sum of Odd Numbers from 1 to 100
To find the sum of odd numbers from 1 to 100, you can use the formula for the sum of an arithmetic series:
Let’s calculate n First;
n= (an – a)/2 + 1
- a = 1 (the first odd number),
- d = 2 (the common difference between consecutive odd numbers), and
- an is the last term of the number.
n= (99-10/2 +1
⇒ n= 98/2 + 1
⇒ n= 49+1
⇒ n= 50
Therefore, n = 50
Let’s use the formula for the sum of an arithmetic series,
Sn = n/2 × (a1 + an)
- Sn is the sum of the series,
- n is the number of terms in the series = 50
- a is the First odd number = 1
- d is the common difference = 2
Sn = 50/2 ×(2×1+(50−1)×2)
⇒ Sn = 25×(2+98)
⇒ Sn = 25×100
⇒ Sn = 2500
The sum of odd numbers from 1 to 100 is also 2500.
Sum of Odd Numbers NOT Starting from 1
Lets say we have to find sum of Odd Numbers N1 to N2 where n1 is not equal to 1, then formula of sum of odd numbers from N1 to N2 is given as
Sum of Odd Numbers Till N2 – Sum of Odd Numbers Till N1
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Sum of Odd Numbers
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.
Table of Content
- What are Odd Numbers?
- How to Find the Sum of Odd Numbers?
- Sum of n Odd Numbers Formula
- Sum of Odd Numbers from 1 to 100
- Solved Examples