What is the sum of the first 683 odd numbers?

Sum of the first 683 odd numbers

"The sum of the first 683 odd numbers" means that we want to add together the first 683 positive odd numbers. The list of the first 683 odd numbers starts with 1 and ends with 1365. Thus, this is what we know:

Numbers = 683
First = 1
Last = 1365

Below is the formula, calculation, and answer to "the sum of the first 683 odd numbers?":

(Numbers/2) x (First + Last)
(683/2) x (1 + 1365)
= 466489

The method above requires us to first figure out what the last number is on the list of the first 683 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 683 odd numbers is:

683² = 466489

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What is the sum of the first 684 odd numbers?
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