A used car is listed for sale at $9000. The price of the car is reduced by 20% for a quick sale. Then it is reduced by 20% of the sale price. What is the final price of the car?

7,000

Step-by-step explanation:

$5,760

Step-by-step explanation:

Start by converting 20% to a decimal, by dividing by 100 = 0.20

Then, multiply 9,000 x 0.20 = 1,800 to get the amount taken off by the sale.

9,000 - 1,800 = 7,200, the first sale price.

Multiply 7,200 by 0.20 = 1,440 to get the amount of the second discount.

7,200 - 1,440 = $5,760, the final price of the car.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt