What is the sum of the first 514 odd numbers?

Sum of the first 514 odd numbers

"The sum of the first 514 odd numbers" means that we want to add together the first 514 positive odd numbers. The list of the first 514 odd numbers starts with 1 and ends with 1027. Thus, this is what we know:

Numbers = 514
First = 1
Last = 1027

Below is the formula, calculation, and answer to "the sum of the first 514 odd numbers?":

(Numbers/2) x (First + Last)
(514/2) x (1 + 1027)
= 264196

The method above requires us to first figure out what the last number is on the list of the first 514 odd numbers. We like the formula method above, but there is an alternate faster way to add up odd numbers. You can get the answer fast by squaring the number. Once again, the sum of the first 514 odd numbers is:

514² = 264196

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What is the sum of the first 515 odd numbers?
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