select the correct answer. jessica opened an apparel shop five years ago. in the first year, she made a…

Answer:

A. $32,400

Explanation:

Step1: Identify the sequence type

This is a geometric - sequence problem. The first - term $a_1 = 3125$ and the common ratio $r=1 + 0.2=1.2$.

Step2: Recall the sum formula for a geometric sequence

The sum formula for a geometric sequence $S_n=\frac{a_1(1 - r^n)}{1 - r}$ where $n$ is the number of terms, $a_1$ is the first - term, and $r$ is the common ratio.

Step3: Substitute the values into the formula

Here, $a_1 = 3125$, $r = 1.2$, and $n = 5$. So $S_5=\frac{3125(1-(1.2)^5)}{1 - 1.2}$.

Step4: Calculate $(1.2)^5$

$(1.2)^5=1.2\times1.2\times1.2\times1.2\times1.2 = 2.48832$.

Step5: Calculate the numerator

$1-(1.2)^5=1 - 2.48832=-1.48832$, and $3125\times(-1.48832)=-4651$.

Step6: Calculate the denominator

$1 - 1.2=-0.2$.

Step7: Calculate the sum

$S_5=\frac{-4651}{-0.2}=32400$.