What is the sum of the first 1537 odd numbers?

Sum of the first 1537 odd numbers

"The sum of the first 1537 odd numbers" means that we want to add together the first 1537 positive odd numbers. The list of the first 1537 odd numbers starts with 1 and ends with 3073. Thus, this is what we know:

Numbers = 1537
First = 1
Last = 3073

Below is the formula, calculation, and answer to "the sum of the first 1537 odd numbers?":

(Numbers/2) x (First + Last)
(1537/2) x (1 + 3073)
= 2362369

The method above requires us to first figure out what the last number is on the list of the first 1537 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 1537 odd numbers is:

1537² = 2362369

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What is the sum of the first 1538 odd numbers?
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