Solve the problem.
-Ms. Patterson proposes to give her daughter Claire an allowance of $\$ 0.05$ on the first day of her 13-day vacation, $\$ 0.10$ on the second day, $\$ 0.20$ on the third day, and so on. Write an equation of a sequence whose terms correspond to Claire's potential allowance. Find the allowance Claire would receive on the last day of her vacation.
A) $a _ { n } = 0.05 ( 2 ) ^ { n } ; \$ 409.60$
B) $a _ { n } = 0.05 n ; \$ 0.65$
C) $a _ { n } = 0.05 + 2 ^ { n - 1 } ; \$ 4096.05$
D) $a _ { n } = 0.05 ( 2 ) ^ { n - 1 } ; \$ 204.80$

Question

Quizplus · Accepted Answer

The sequence follows a geometric progression where each term is double the previous term, starting from $0.05. 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, $a_1 = 0.05$ and $r = 2$, so the formula is $a_n = 0.05 \cdot 2^{(n-1)}$. On the 13th day, the allowance is $0.05 \cdot 2^{(13-1)} = 0.05 \cdot 2^{12} = 0.05 \cdot 4096 = \$204.80$.

Solve the Problem $0.05\$ 0.05$0.05 On the First Day of Her 13-Day Vacation

Solve the Problem $\$ 0.05$ On the First Day of Her 13-Day Vacation