The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week, the dealership sold three cars ([tex]P_0 = 3[/tex]). The second week, the dealership sold seven cars ([tex]P_1 = 7[/tex]).

Write the recursive formula for the number of cars sold, [tex]P_n[/tex], in the (n + 1)th week.

Question

12-09-2024
Mathematics

College

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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 three cars ([tex]P_0 = 3[/tex]). The second week, the dealership sold seven cars ([tex]P_1 = 7[/tex]).

Write the recursive formula for the number of cars sold, [tex]P_n[/tex], in the (n + 1)th week.

Answer :

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coolSky61 coolSky61 · Answer 1 · 2023-11-25T01:40:46-05:00

Final answer:

The recursive formula for the number of cars sold in the (n + 1)th week is Pₙ = Pₙ₋₁ + d, where Pₙ₋₁ is the number of cars sold in the previous week and d is the common difference.

Explanation:

The number of cars sold weekly by a new automobile dealership can be represented by a linear growth model. Given that the dealership sold 3 cars in the first week (P₀ = 3) and 7 cars in the second week (P₁ = 7), we need to derive the recursive formula for the number of cars sold, Pₙ, in the (n + 1)th week.

Since the growth is linear, we can find the common difference, d, by subtracting the number of cars sold in the first week from the second week: d = P₁ - P₀ = 7 - 3 = 4.

The recursive formula for the number of cars sold in the (n + 1)th week, Pₙ, can be written as: Pₙ = Pₙ₋₁ + d, where Pₙ₋₁ represents the number of cars sold in the nth week and d is the common difference.

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