7. When Luis opened a mechanics shop, his total revenue, in thousands of dollars, was 2.1 in his first year. Each following year, his rate of growth of the total revenue has been 28%. Some of the revenue data for his shop is shown in the table.

Question

Year 1 2 3 4
Total Revenue

(In Thousands of Dollars)

2.1 2.688 3.44 4.04
Complete the statement.


(1 point)
The scenario is best represented by
a geometric sequence
.
Question 3
8. A sequence is shown.

1400, 560, 224, 89.6, 35,84,.....

Complete the explicit formula for the sequence.

(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
an=
Response area. Response area(n−1)

Answer 1

For Question 7, the scenario where Luis's total revenue grows each year by a consistent percentage (28%) can be classified as a geometric sequence. In geometric sequences, each term after the first is found by multiplying the previous term by a constant (the common ratio).

For Question 8, we need to identify the explicit formula for the sequence provided. The numbers given are: 1400, 560, 224, 89.6, 35.84...

To determine the explicit formula, first, we recognize that this is a decreasing geometric sequence where each term is multiplied by a common ratio.

To find the common ratio (r):

• From the first term (1400) to the second term (560): \[ r = \frac{560}{1400} = 0.4 \]

It's consistent for the rest of the sequence as well:

• From the second term (560) to the third term (224): \[ r = \frac{224}{560} = 0.4 \]

The explicit formula for a geometric sequence can be expressed as: \[ a_n = a_1 \cdot r^{(n-1)} \] where \( a_1 \) is the first term and \( r \) is the common ratio.

In this case:

• \( a_1 = 1400 \)
• \( r = 0.4 \)

Thus, the explicit formula is: \[ a_n = 1400 \cdot (0.4)^{(n-1)} \]

So in the response areas: an = \( 1400 \) Response area = \( 0.4 \) (n - 1)

This gives us the complete explicit formula for the sequence: \[ a_n = 1400 \cdot (0.4)^{(n-1)} \]