Question

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?

Answer 1

Answer:

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