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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.

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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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Calculate the sum of an arithmetic sequence with the formula (n/2)(2a + (n-1)d). The sum is represented by the Greek letter sigma, while the variable a is the first value of the sequence, d is the difference between values in the sequence, and n is the number of terms in the series.