Pythagorean Odds

Algebra Level 1

Consider the following sequence of all positive odd numbers: \(1, 3, 5, 7, 9, 11, 13, \ldots.\)

The sum of the first 3 terms is equal to 9: \(1+3+5=9.\)
The sum of the first 5 terms is equal to 25: \(1+3+5+7+9=25.\)

What is the sum of the first 99 terms of the sequence?

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