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Consecutive Numbers
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| Submitted: Thu Jul 11 2002
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Consecutive Numbers Someone tells you that it is possible to make any number by writing an addition sum using only consecutive numbers. E.g. 18 = 3+4+5+6 21 = 6+7+8 Is this person right? Can you make every number like this? Investigate this idea and write down anything you notice as you go along. I am now going to show you some examples. 1 = 0+1 2 = DOESN'T WORK! 3 = 1+2 4 = DOESN'T WORK! 5 = 2+3 6 = 1+2+3 7 = 3+4 8 = DOESN'T WORK! 9 = 4+5 10 = 1+2+3+4 Etc. I am now going to prove this algebraically.> If the 1st number is N, the 2nd is N+1. This gives you 2N+1 2N+1 = 1,3,5,7,9,11,13,15 etc. All odd numbers.> If the 1st number is N, the 2nd is N+1, the 3rd is N+2. This gives you 3N+3. 3N+3 = 6,9,12,15,18,21 etc. Every third number.> If the 1st number is N, the 2nd is N+1, the 3rd is N+2, the 4th is N+3. This gives you...
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