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The first three elements of a number sequence are 1, 2, 3. ( As you can see, the middle number is one less than the product of its neighbors. This is true for the rest of the elements of this sequence. Now add the elements of the sequence up to a certain element. Could this sum be 2009? Could this sum be 2010?

  • Math -

    the sequence runs this way :
    1 2 3 2 1 1 2 3 ..
    it repeats!

    the first loop is 1 2 3 2 1
    the sum of that loop is 9
    so as long as we add up to the end of a loop we have multiples of 9
    If we add up 223 loops the sum is 2007
    adding the next digit, which is a 1 would give up 2008, and if we add the next one after that, we would get 2010

    So it is not possible for a sum of 2009, but we will reach 2010

  • Math -

    THANK YOU! =)

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