Since the soup kitchen starts with 16 gallons and there are 128 ounces in 1 gallon, then the first term of the sequence is
Three-fourths of the soup is left after each day if only a quarter of the soup is served and the remainder is saved for the following day. The next terms in the sequence can then be found by multiplying each term by to get the next term. The sequence's subsequent four terms are then:
The sequence's first five terms are then 2048,1536,1152,864,648.
Since the terms have a common ratio of , then the sequence is geometric. The formula for the nth term of a geometric sequence is . Since and , then the equation that represents the nth term of the sequence is
To finish all of the soup, you would need an=0 for some value of n. Multiplying a number by repeatedly will give a smaller and smaller number each time you multiply. The number will never equal 0 though, it will just get very close to 0. Therefore, the soup will never be gone.
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