a The formula for the nth term of a geometric sequence is a_n=a_1r^(n-1).
B
b Substitute the given value into the function you wrote in Part A.
C
c Use the answer in Part B.
A
a a_n=0.01(2)^(n-1)
B
b $167 772.16
C
c No, see solution.
Practice makes perfect
a Let's start by making a table that shows the amount of money the student pays her family each day.
We see that there is a common ratio of 2 between each pair of consecutive terms. We can write an equation that represents the nth term of this geometric sequence, since a_1= 0.01 and r= 2.
a_n= a_1( r)^(n-1) ⇔ a_n= 0.01( 2)^(n-1)
b To find the amount of money she pays on the 25th day, we will substitute 25 in the formula we write in Part A.
c In Part B, we have showed that she had to pay thousands of dollars before a month is over. It also doubles itself every day, so soon it will be in the millions of dollars. Therefore, the students did not make a good choice. She should have chosen to live on campus.
