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# What is the sum of the first 100 odd numbers?

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The sum of the first 100 odd numbers is 10,000. There are 100 odd numbers between 1 and 199, and each pair from the start and end of the sequence (e.g. 1 and 199, 3 and 197, etc.) adds up to 200. Multiplying 50 times 200 equals 10,000.

## Keep Learning

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Odd numbers are defined by their parity, which is the property that makes every integer either even or odd. All odd numbers have a parity of 1, while all even numbers have a parity of 2. Any set of odd numbers can be found by using odd = {2k + 1 : k therefore Z}.

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## Related Questions

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The distributive property is a mathematical and algebraic property that says that multiplying two numbers is the same as multiplying one of those numbers by the sum of the other number's parts. In arithmetic, 50 x 45 is equal to (50 x 40) + (50 x 5). In algebra, the property is shown as x(y + z) = xy + xz.

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The numbers to add in an addition problem are called addends, summands or terms, while the answer to the problem is the sum. In the number sentence a+b=c, a and b are addends, while c is the sum.

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Estimate a sum by rounding it to the greatest place value by completing three steps. First, round each value in the equation to the greatest place value. Second, add together the numbers in the greatest place values by reducing the numbers to single digits. Third, convert the single digits back into the original place values.