Question

buying one movie ticket online costs $16.50, two tickets cost $30.50, and three tickets cost $44.50 assuming that the relationship is linear, write recursive and explicit formulas to represent the cost of buying $n$ tickets online. explain why the relationship is likely to be linear
recursive $a_n = a_{n-1}$ + choose..., $a_1$ = choose
explicit $a_n$ = choose + choose $n$
the relationship is linear because choose...

Explanation:

Step1: Find common difference d

$d = 30.50 - 16.50 = 14.00$

Step2: Set recursive formula

Recursive formula: $a_n = a_{n-1} + d$, $a_1 = 16.50$

Step3: Derive explicit formula

Explicit formula: $a_n = a_1 + (n-1)d = 16.50 + 14(n-1) = 2.50 + 14n$

Step4: Explain linear relationship

The cost increases by a constant amount per ticket.

Answer:

recursive: $a_n = a_{n-1} + 14.00$, $a_1 = 16.50$
explicit: $a_n = 2.50 + 14.00n$
The relationship is linear because the cost increases by a constant amount with each additional ticket.