The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold six cars (P 0 = 6). The second week the dealership sold eight cars (P 1 = 8). Write the recursive formula for the number of cars sold, P n, in the (n + 1) th week. P n = P n - 1 + Write the explicit formula for the number of cars sold, P n, in the (n + 1) th week. P n = If this trend continues, how many cars will be sold in the fourth week?

Recursive Formula, Pₙ=Pₙ₋₁+2

Explicit Formula, Uₙ=4+2n

12 cars

Step-by-step explanation:

In Week 1, the dealer sold six cars, P₀=6

In Week 2, the dealer sold 8 cars, P₁=8

The difference in car sales between the first and second week is 2.

Therefore, for the (n+1) th week, the Recursive Formula is Pₙ=Pₙ₋₁+2

This is an arithmetic progression where the:

First term, a=6

Common difference, d = 2

The nth term of an A. P. is given by Uₙ=a + (n-1) d.

The Explicit Formula, Uₙ=6+2 (n-1)

=6+2n-2=4+2n

In the fourth week, U₄=4+2 (4) = 4+8=12

12 cars will be sold in the fourth week