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
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
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Solution
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, $P_n = 4 + 6(6-1) = 34$.