Using the formula for the sum of an arithmetic sequence;
Sum = 1/2*n [n is the total number of terms] *(2a [a is the value of the first term] + (n-1) * d)[d is the common difference between each term]
So the formula looks like this: Sum = 1/2*n (2a+(n-1)*d)
n = 50 because there's 50 odd numbers in a hundred and 50 even numbers (50+50=100)
a = 1
d = 2
So inputting the values gives:
Sum= 1/2*50 (2*1+(50-1)* 2)
Sum= 25*(2+49*2)
Sum= 25*(2+98)
Sum= 25*(100)
Sum= 2500
Answer= 2,500
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The sum of all the odd numbers from 1 through 100 is 10,000
The sum of the first 100 odd numbers (1 through 199) is 10000 (ten thou)
100
No 5 odd numbers add up to 100. The sum of any two odd numbers is even. The sum of any two even numbers is even. So the sum of any 4 odd numbers must be even. Take that and add an odd number and the sum must be odd. Therefore, the sum of any 5 odd numbers must be odd. 100 is even. In conclusion: The sum of any odd number of odd numbers is odd.
The sum of all the odd numbers between 1 and 12000 is 36000000.