Solve the problem.
-Suppose that an individual is paid $0.02 on day 1 and every day thereafter, the payment is doubled.
a. Write a formula for the nth term of a sequence that gives the payment (in $) on day n.
b. How much will the individual earn on day 10? day 20?
A) a. $a _ { n } = 0.02 ( 2 ) ^ { n - 1 }$
b. $\$ 10.24$ on day $10 , \$ 10,485.76$ on day 20
B) a. $a _ { n } = 0.02 ( 2 ) ^ { n }$
b. b. $\$ 40.94$ on day $10 , \$ 41,943.02$ on day 20
C) a. $a _ { n } = 0.02 ( 2 ) ^ { n - 1 }$
b. $\$ 20.46$ on day $10 , \$ 20,971.5$ on day 20
D) a. $a _ { n } = 0.02 ( 2 ) ^ { n }$
b. b. $\$ 20.48$ on day $10 , \$ 20,971.52$ on day 20

Question

Solve the problem.
-Suppose that an individual is paid $0.02 on day 1 and every day thereafter, the payment is doubled. 
a. Write a formula for the nth term of a sequence that gives the payment (in $) on day n.
b. How much will the individual earn on day 10? day 20? 
A) a. $a _ { n } = 0.02 ( 2 ) ^ { n - 1 }$
b. $\$ 10.24$ on day $10 , \$ 10,485.76$ on day 20
B) a. $a _ { n } = 0.02 ( 2 ) ^ { n }$
b. b. $\$ 40.94$ on day $10 , \$ 41,943.02$ on day 20
C) a. $a _ { n } = 0.02 ( 2 ) ^ { n - 1 }$
b. $\$ 20.46$ on day $10 , \$ 20,971.5$ on day 20
D) a. $a _ { n } = 0.02 ( 2 ) ^ { n }$
b. b. $\$ 20.48$ on day $10 , \$ 20,971.52$ on day 20

Quizplus · Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$, where $a_1$ is the first term and $r$ is the common ratio. Here, $a_1 = 0.02$ and $r = 2$, so $a_n = 0.02 \cdot 2^{(n-1)}$. On day 10, the payment is $0.02 \cdot 2^{9} = \$10.24$, and on day 20, it is $0.02 \cdot 2^{19} = \$10,485.76$.

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