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The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold two cars \((P_0 = 2)\). The second week the dealership sold seven cars \((P_1 = 7)\).

1. Write the recursive formula for the number of cars sold, \(P_N\), in the \((N+1)\)th week.
\[
P_N = P_{N-1} + 5
\]

2. Write the explicit formula for the number of cars sold, \(P_N\), in the \((N+1)\)th week.
\[
P_N = 5N + 2
\]

3. If this trend continues, how many cars will be sold in the sixth week?
\[
P_6 = 5(6) + 2 = 32 \text{ cars}
\]

Answer :

The dealership sold two cars in the first week and five more cars each subsequent week. The formulas may differ in other situations or if the trend changes.

The recursive formula for the number of cars sold in the (N+1)th week is P(N) = P(N-1) + 5.

In this case, P(N) represents the number of cars sold in the (N+1)th week, and P(N-1) represents the number of cars sold in the Nth week.

The explicit formula for the number of cars sold in the (N+1)th week is P(N) = N + 2.

Here, N represents the week number, and by adding 2 to it, we can determine the number of cars sold in that week.

To find out how many cars will be sold in the sixth week, we can substitute N=5 into the explicit formula.

P(5) = 5 + 2 = 7

Therefore, if the trend continues, 7 cars will be sold in the sixth week.

Keep in mind that these formulas are specific to the given situation, where the dealership sold two cars in the first week and five more cars each subsequent week. The formulas may differ in other situations or if the trend changes.

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