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.
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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
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
Question: What is the sum of the first 10 odd numbers?
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.
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)
Therefore, the Sum of the first odd numbers is 100
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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