What is the sum of all odd numbers between 0 and 100?

Braden Miranda

Braden Miranda

Answered question

2023-02-15

What is the sum of all odd numbers between 0 and 100?

Answer & Explanation

Jessica Henry

Jessica Henry

Beginner2023-02-16Added 4 answers

Determine the sum of all odd numbers between0and100.
Any number that cannot be divided by two is referred to as an odd number. In other words, several forms2k+1, where kZ (i.e. integers) are called odd numbers.
The sum of the odd numbers are =1+3+5+7+9+.+93+95+97+99
For any arithmetic Progression (A.P.):
T(n)=a+(n1)d
Where,
a is the first time
d is difference
.n is the number of terms.
T(n)orl is nth term
Here, the odd number between 0and100 which 1,3,5,7,9,.,93,95,97,99 are in A.P.
where,
a=1l=99d=2
So, Calculate the no. of the term (n) in A.P.:
T(n)=a+(n1)d99=1+(n1)298=2n2100=2nn=50
Calculate the sum of the terms 1+3+5+7+9+.+93+95+97+99 which is in A.P. is as follows:
S(n)=n2(a+l)(n=50)S(n)=502(1+99)S(n)=502×100S(n)=50×50S(n)=2500
Therefore, the sum of all odd numbers between 0and100 is2500.

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