A soup kitchen makes 16 gallons of soup. Each day, a quarter of the soup is served and the rest is saved for the next day. Write the first five terms

sjeikdom0 2021-03-08 Answered
A soup kitchen makes 16 gallons of soup. Each day, a quarter of the soup is served and the rest is saved for the next day. Write the first five terms of the sequence of the number of fluid ounces of soup left each day. Write an equation that represents the nth term of the sequence. When is all the soup gone?
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Expert Answer

cyhuddwyr9
Answered 2021-03-09 Author has 90 answers

Since the soup kitchen starts with 16 gallons and there are 128 ounces in 1 gallong, then the first term of the sequence is a1=16(128)=2048.
If a quarter of the soup is served and the rest is saved for the next day, then three-fourths of the soup is left after each day. The next terms in the sequence can then be found by multiplying each term by 34 to get the next term. The next four terms of the sequence are then:
a2=34a1=34(2048)=1536
a3=34a2=34(1536)=1152
a4=34a3=34(1152)=864
a5=34a4=34(864)=648
The first five terms of the sequence are then 2048,1536,1152,864,648.
Since the terms have a common ratio of r=34, then the sequence is geometric. The formula for the nnth term of a geometric sequence is an=a1rn1. Since a1=2048 and r=34, then the equation that represents the nnth term of the sequence is an=2048(34)n1
For the soup to be all gone, you would need an=0 for some value of nn. Multiplying a number by 34 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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