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

select the correct answer.\njessica opened an apparel shop five years ago. in the first year, she made a profit of $3,125. each year after that, her profit was 20 percent more than in the previous year. what is the total profit jessica earned in 5 years?\na. $32,400\nb. $23,255\nc. $7,776\nd. $6,480

select the correct answer.\njessica opened an apparel shop five years ago. in the first year, she made a profit of $3,125. each year after that, her profit was 20 percent more than in the previous year. what is the total profit jessica earned in 5 years?\na. $32,400\nb. $23,255\nc. $7,776\nd. $6,480

Answer

Explanation:

Step1: Identify the geometric - series formula

The profit forms a geometric series with first - term $a = 3125$ and common ratio $r=1 + 0.2=1.2$. The sum of the first $n$ terms of a geometric series is given by $S_n=\frac{a(r^n - 1)}{r - 1}$ when $r\neq1$, where $n = 5$, $a = 3125$, and $r = 1.2$.

Step2: Substitute the values into the formula

$S_5=\frac{3125\times(1.2^5 - 1)}{1.2 - 1}$. First, calculate $1.2^5=1.2\times1.2\times1.2\times1.2\times1.2 = 2.48832$. Then, $1.2^5-1=2.48832 - 1=1.48832$. Next, $S_5=\frac{3125\times1.48832}{0.2}$. $3125\times1.48832 = 4651$. Finally, $\frac{4651}{0.2}=23255$.

Answer:

B. $$23,255$