The ticket gate at a haunted corn maze start with $80 in the cash box. they charge $8 per person

write a recursive formula for the amount of money in the cash box after n peope paid

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