Questions: The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold four cars (P0=4). The second week the dealership sold cars (P1=10). Write the recursive formula for the number of cars sold, Pn, in the (n+1)th week. Pn=Pn-1+ Write the explicit formula for the number of cars sold, Pn, in the (n+1)th week. Pn= If this trend continues, how many cars will be sold in the sixth week? cars

The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold four cars (P0=4). The second week the dealership sold cars (P1=10).

Write the recursive formula for the number of cars sold, Pn, in the (n+1)th week.
Pn=Pn-1+

Write the explicit formula for the number of cars sold, Pn, in the (n+1)th week.
Pn=

If this trend continues, how many cars will be sold in the sixth week?
cars
Transcript text: The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold four cars $\left(P_{0}=4\right)$ : The second week the dealership sold cars $\left(P_{1}=10\right)$. Write the recursive formula for the number of cars sold, $P_{n}$, in the $(n+1)^{\text {th }}$ week. \[ P_{n}=P_{n-1}+ \] $\square$ Write the explicit formula for the number of cars sold, $P_{n}$, in the $(n+1)^{\text {th }}$ week. \[ P_{n}= \] $\square$ If this trend continues, how many cars will be sold in the sixth week? $\square$ cars Question Help: Video Message instructor Calculator Submit Question
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Solution

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Solution Steps

Step 1: Identify the Initial Value

The initial number of cars sold in the first week, $P_0$, is 4.

Step 2: Calculate the Common Difference

The constant increase in the number of cars sold each week, $d$, is 6.

Step 3: Use the Explicit Formula

Using the explicit formula $P_n = P_0 + d(n-1)$, we calculate the number of cars sold in week 6. Substituting the given values, $P_n = 4 + 6(6-1) = 34$.

Final Answer:

The number of cars sold in week 6 is 34 cars.

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