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2500
The sum of the first 8 odd numbers is 64.
The sum of the first 600 odd numbers is 360,000.
The sum of the first 8,000 odd numbers 64,000,000.
The sum of the first 1,000 odd numbers is 1,000,000.
Let's talk this out and see if we can work it out. The sum of the first N odd integers means, 1+3+5+7+9+11+... Where N is how many odd numbers we're adding. Let's choose numbers for N, and see if we can find a pattern. N=1 --> 1 (sum of the first odd integer) N=2 --> 1 + 3 = 4 (sum of the first 2 odd integers) N=3 --> 1 + 3 + 5 = 9 (sum of the first 3 odd integers) N=4 --> 1 + 3 + 5 + 7 = 16 Do you notice a pattern yet? Take a look at when N = 2, what is the sum? That's right, 4! and when N = 3... the sum is 9. N = 4 the sum is 16.... I see a pattern, do you? Answer: If you don't, you'll notice that the sum of the first N odd integers is always = N2
9801 * The sum of the first two odd numbers (1+3) is 4, or 22 * The sum of the first three odd numbers (1+3+5) is 9, or 32 * The sum of the first four odd numbers (1+3+5+7) is 16, or 42 * ...and so on So the sum of the first 99 odd numbers, using the pattern above, would be 992 or 9801.
2500
The sum of the first 15 odd numbers is 225.
The sum of the first 100 odd numbers is 10,000.
The sum of the first 300 odd numbers is 90,000
The sum of the first 40 odd numbers is 1,600.
The sum of the first 8 odd numbers is 64.
The sum of the first 600 odd numbers is 360,000.
The sum of the first 8,000 odd numbers 64,000,000.
The sum of the first 1,000 odd numbers is 1,000,000.
The sum of the first 50 odd numbers is 2,500.