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

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Part 1
A.
180 ft
B.
250 ft
C.
270 ft
D.
230 ft

Answer 1

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