Mr. John Roosevelt asked the class
to see if they could find the sum of the first 50 odd numbers. As everyone
settled down to their addition, Gabriel ran to him and said, 'The sum is
2,500.' Ms. John Roosevelt thought, 'Lucky guess,' and gave him the task of
finding the sum of the first 75 odd numbers. Within 20 seconds, Gabriel was
back with the correct answer.
How does Gabriel find the sum so quickly and what is the answer?
How does Gabriel find the sum so quickly and what is the answer?
Answer:
The following pattern holds:
The sum is equal to n * n, when n is the number of consecutive odd numbers, starting with 1.
For example, the sum of the first 3 odd numbers (1+3+5) is equal to 3 * 3, or 9. The sum of the first 4 odd numbers (1+3+5+7) is equal to 4 * 4, or 16. The sum of the first 5 odd numbers is equal to 5 * 5, or 25; and so on.
The sum is equal to n * n, when n is the number of consecutive odd numbers, starting with 1.
For example, the sum of the first 3 odd numbers (1+3+5) is equal to 3 * 3, or 9. The sum of the first 4 odd numbers (1+3+5+7) is equal to 4 * 4, or 16. The sum of the first 5 odd numbers is equal to 5 * 5, or 25; and so on.
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