Question

Arithmetic Sequence Formula: An = d(n-1)+ a1, A movie rental club charges $4.95 for the first month's rentals. The club charges $12.95

for each additional month. Use the arithmetic sequence formula to write an equation to
represent the sequence. Then, find the total cost for one year.

Answer 1

The arithmetic sequence formula is An = d(n-1) + a1. The equation representing the sequence in this case is An = 12.95(n-1) + 4.95. The total cost for one year is $162.75.

Step-by-step explanation:

The arithmetic sequence formula is: An = d(n-1) + a1, where An represents the nth term, d is the common difference, and a1 is the first term.

In this case, the first month's rental fee is $4.95, so a1 = $4.95. The additional monthly fee is $12.95, so d = $12.95.

Therefore, the equation representing the sequence is An = 12.95(n-1) + 4.95.

To find the total cost for one year, we need to find the sum of all the monthly fees for 12 months. This can be done by substituting n = 12 into the equation and simplifying.

Thus, the total cost for one year is: A12 = 12.95(12-1) + 4.95 = $162.75.