There are 899 three digit numbers (100 through 999).
Each century (grouping of 100 numbers) has 50 odd numbers. (half of the numbers are odd, half are even)
So.. 100-199, 200-299, 300-399, 400-499, 500-599, 600-699, 700-799, 800-899, 900-999
We have 9 centuries.
Number of odd numbers = 9*50 = 450
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450
450
450 whole numbers.
There are 17 such numbers.
The sum of the first 450 consecutive odd numbers is 450 squared or 202,500.