You have a gift card for a coffee shop worth $90. Each day you use the card to get a coffee for $4.10. Write an explicit formula to represent the amount of money available as an arithmetic sequence. What is the value of the card after you buy your 8th coffee?

Answer: The value of the card after you buy your 8th coffee will be $61.3

Step-by-step explanation:

The worth of the gift card for the coffee shop is $90. Each day you use the card to get a coffee for $4.10. This means that the worth of the gift card is reducing by $4.10 each day. This rate is in arithmetic progression.

The formula for the nth term of an arithmetic sequence, Tn is expressed as

Tn = a + (n-1) d

Where a is the first term

d is the common difference

n is the number of days

From the information given,

a = $90

d = - $4.1

The explicit formula representing the amount of money available will be

Tn = 90 - 4.1 (n - 1)

The value of the card after you buy your 8th coffee will be

T8 = 90 - 4.1 (8 - 1) = T8 = 90 - 4.1*7

T8 = 90 - 28.7

T8 = $61.3