# Sum of Odd Numbers Calculator

Free handy tool Sum of Odd Numbers Calculator is designed to provide the sum of odd numbers easily. All you need to do is enter the input n in the input section to get the concerned output in no time.

##### Sum of Odd Numbers Calculator
Input (n)

Sum of Odd Numbers Calculator: Are you scared of finding the Sum of Odd Numbers? Fear Not! and make use of our handy tool to find the Sum of Odd Numbers. Our Calculator is designed in such a way that people of any mathematical knowledge can solve the problems on the sum of Odd Numbers effortlessly. In addition, you can get accurate and straightforward descriptions explaining the concept in a much better way.

## Procedure to Solve the Sum of Odd Numbers

Go through the following guidelines on how to find the Sum of Odd Numbers. They are two formulas to figure out the sum of odd numbers.

The formula is given by S = (Numbers/2)*(First Digit + Last Digit)

In the above case, you need to figure out the first and last digit of the list of odd numbers given. If you feel it a bit difficult you can go with an easier way of finding the sum of odd numbers. It is just by squaring the numbers given to you. Have a look at how the formula arrived in the below modules.

Let the sum of odd numbers be Sn = 1+3+5+7+9+…………………..+(2n-1) ……. (1)

As per Arithmetic Progression for any series, we know the sum of numbers is

Sn=1/2×n[2a+(n-1)d] ……(2)

n is the number of digits in the series

a is the first term of the A.P

d is the common difference

If we place the values in equation 2 with respect to equation 1 we get as follows

a = 1, d = 2

Consider the last term as l = (2n-1)

Sn = ( n/2) × (a+l )

Sn = (n/2) × (1 + 2n – 1)

Sn = (n/2) × (2n) = n2

S = n2

Therefore, the Sum of Odd Numbers can be found using the simple formula n2

Example

Question: What is the sum of the first 10 odd numbers?

Solution:

Method 1

The formula to find the sum of odd numbers = n2

In this case, n = 10

Simply, substitute in the formula = 102

Thus, the sum of the first 10 odd numbers is 100.

Method 2

You can find the same using the other formula. The list of first 10 odd numbers begin with 1 and 19 as we all know

Sum of Odd Numbers Formula = (Numbers/2)*(First digit+Last Digit)

Numbers = 10

First Digit = 1

Last Digit = 19

Replacing the values in the sum of odd numbers = (10/2)*(1+19)

=5*20

=100

Therefore, the Sum of the first odd numbers is 100 ### FAQs on Sum of Odd Numbers Calculator

1. What is the formula to calculate the sum of odd numbers?

There are two formulas to calculate the sum of odd numbers i.e. S = n2 or (Numbers/2)*(First digit+Last Digit).

2. How to find the Sum of Odd Numbers using a Calculator?

Simply enter the input number n for which you want to find the Sum of Odd Numbers and click the Calculate Button to get the result in no time.

3. Where do I get Solved Examples on finding the Sum of Odd Numbers?

You can get Solved Examples on finding the Sum of Odd Numbers on our page.

4. Is there any Online Portal that provides the best tool for the Sum of Odd Numbers?

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