Answer:
The correct answer is aₙ = aₙ₋₁ + 8 when a₁ = 80 and n ≥ 2
Step-by-step explanation:
1. Let's review all the information provided for solving this question:
Amount of money in the cash box at the ticket gate when it opens = US$ 80
Amount of money that every visitor to the haunted corn maze pays (ticket) = US$ 80
Number of people paying the ticket to the haunted corn maze = n
Amount of money in the cash box at any moment after the opening = x
2. Let's write the recursive formula for the amount of money in the cash box (x)
aₙ = aₙ₋₁ + 8 when a₁ = 80 and n ≥ 2
Let's prove it for n = 2, n= 3 and n = 4
a₂ = aₙ₋₁ + 8 = a₁ + 8 = 80 + 8 = 88
a₃ = aₙ₋₁ + 8 = a₂ + 8 = 88 + 8 = 96
a₄ = aₙ₋₁ + 8 = a₃ + 8 = 96 + 8 = 104
