There are 52 blades of grass in 2 in^2 of lawn. there are 580 blades of grass in 8 in^2 of the same lawn. which equation models

Response:

B: 32 cm

To clarify, one should only sum the external measurements

6+6+4+4+3+3+3+3=32 cm

a) The sequence is geometric.

b) The subsequent term is 486

c) The rule is:

The 20th term will be: a_{20}=6973568802

Step-by-step explanation:

The series 6, 18, 54, 162, ... depicts the number of push-ups Kendall performed each week, starting from her initial week of exercise.

Part a) Is this sequence arithmetic or geometric?

An arithmetic sequence has a constant difference between consecutive terms.

In the given series 6, 18, 54, 162,

18-6 = 12

54-18= 36

The differences are not constant, thus it isn’t arithmetic.

A geometric sequence maintains a constant ratio between consecutive terms.

In this series 6, 18, 54, 162,

18/6 = 3

54/18 = 3

162/54 = 3

The ratios remain constant; therefore, the sequence is geometric.

The sequence in question is geometric.

Part b) How can you determine the next number in the series?

The next number can be calculated using the following formula:

where a_n= nth term

a= first term

r= common ratio

The next number represents the 5th term of the sequence.

To find the 5th term:

Thus, the next term in the sequence is 486

Part c) What is the rule for determining the 20th week? Calculate the 20th week.

The rule for determining the 20th week is:

Here n=20

Calculating the 20th week

Ratio: Red: Total 2: 5 (x2) 4: 10. Green: Total 3: 10. The aggregate of red and green marbles is 4 + 3 = 7. Therefore, Blue marbles = 10 - 7 = 3. This gives us a breakdown of 10 parts equating to 40 marbles and consequently, 1 part = 40 ÷ 10 = 4 leading to 3 parts = 4 x 3 = 12. Final answer: There are 12 blue marbles.

The entire sequence is: 88511, 16351, 73155, 10251

Solution:

The sequence provided is:

88511, 16351,?, 10251

Utilizing basic mathematical operations (+, -, ×, /) allows us to determine the missing number.

Let’s break down the logic behind this sequence

Examining the initial term of the series 88511

8 + 8 = 16

8 - 5 = 3

5 × 1 = 5

1 / 1 = 1

Merging these digits results in 16351, which is the second term in the series

Therefore, the underlying method is:

Add the first two digits in 8851

Subtract the third digit from the second digit

Multiply the third and fourth digits

Divide the fourth digit by the fifth digit

Following the same pattern allows us to identify the missing term

Next, consider the second term 16351 in the series

1 + 6 = 7

6 - 3 = 3

3 × 5 = 15

5 / 1 = 5

By combining these digits, we arrive at 73155, which follows as the next term in the series

Therefore, the missing term in the series is 73155

The complete series is: 88511, 16351, 73155, 10251