Question
The distance, in feet, that a car travels down the side of a mountain in each consecutive second is modeled by a sequence whose general term is a Subscript n Baseline equals 50 n minus 20, where n is the number of seconds. Find the distance the car travels in the fifth second.
Question content area bottom
Part 1
A.
180 ft
B.
250 ft
C.
270 ft
D.
230 ft
Question content area bottom
Part 1
A.
180 ft
B.
250 ft
C.
270 ft
D.
230 ft
Answers
GPT-4o mini
To find the distance the car travels in the fifth second, we can use the given formula for the distance traveled in the \( n \)-th second:
\[
d_n = 50n - 20
\]
Now, we need to find \( d_5 \) (the distance traveled in the fifth second):
\[
d_5 = 50(5) - 20
\]
Calculating this step-by-step:
1. Calculate \( 50(5) = 250 \)
2. Then subtract 20: \( 250 - 20 = 230 \)
So, the distance the car travels in the fifth second is:
\[
d_5 = 230 \text{ ft}
\]
Thus, the correct answer is:
**D. 230 ft**
\[
d_n = 50n - 20
\]
Now, we need to find \( d_5 \) (the distance traveled in the fifth second):
\[
d_5 = 50(5) - 20
\]
Calculating this step-by-step:
1. Calculate \( 50(5) = 250 \)
2. Then subtract 20: \( 250 - 20 = 230 \)
So, the distance the car travels in the fifth second is:
\[
d_5 = 230 \text{ ft}
\]
Thus, the correct answer is:
**D. 230 ft**