Question

a car travels 150 kilometers on the first day of a road trip. with each subsequent day, the car covers 92% of the distance covered on the previous day. what is the total distance the car has traveled after completing their 8th day? round your answer to the nearest kilometer.

select one:
a. 910 kilometers
b. 913 kilometers
c. 829 kilometers
d. 840 kilometers

Explanation:

Step1: Identify geometric series parameters

First term $a_1 = 150$, common ratio $r = 0.92$, number of terms $n = 8$

Step2: Apply finite series sum formula

Use $S_n = a_1 \cdot \frac{1 - r^n}{1 - r}$

Step3: Calculate $r^n$ value

$0.92^8 \approx 0.5132$

Step4: Compute numerator and denominator

$1 - 0.5132 = 0.4868$; $1 - 0.92 = 0.08$

Step5: Solve for total distance

$S_8 = 150 \cdot \frac{0.4868}{0.08} = 150 \cdot 6.085 = 912.75$

Step6: Round to nearest kilometer

$912.75 \approx 913$

Answer:

B. 913 kilometers