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Randy had a sheep that started eating more and more as each day passed.On July 1,Randy’s sheep ate 5 carrots. On July 2,Randy’s sheep ate 11 carrots. On July 3, the sheep ate 18 carrots. How many carrots will the hungry sheep eat on July 30th?

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    Note that the differences grow by one each day. That implies a quadratic relationship. In fact

    on July nth, the sheep eats n(n+9)/2 carrots.

    On July 30, that's 30(39)/2 = 15*39 = 585 carrots

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