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

Multiple Choice

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) $a _ { n } = 0.05 ( 2 ) ^ { n - 1 } ; \$ 204.80$