hi im really stuck...
3. which explains why the sequence 81,3,1/9....... is arithmric or geometric
A. the sequence is arithmic because it decreases by a factor of 1/27
B. the sequence is geometric because it dereases by a factor of 1/27
C. the sequence is arithmeric because it decreases by a factor of 3
D. the sequence is geometric because it decreases by a factor of 3
3 / 81 = 3 / 3 ∙ 27 = 1 / 27
( 1 / 9 ) / 3 = 1 / 27
Answer B.
The sequence is geometric because it decreases by a factor of 1 / 27
To determine whether the sequence 81, 3, 1/9... is arithmetic or geometric, we need to analyze the pattern of the numbers.
- An arithmetic sequence is a sequence in which each term is obtained by adding or subtracting a constant value called the "common difference" to the previous term.
- A geometric sequence, on the other hand, is a sequence in which each term is obtained by multiplying or dividing the previous term by a constant value called the "common ratio".
Let's look at the given sequence: 81, 3, 1/9...
First, we can determine if the sequence is arithmetic by checking if there is a common difference between consecutive terms.
To find the common difference, we subtract each term from its consecutive term:
3 - 81 = -78
1/9 - 3 = -26/9
As we can see, the differences between consecutive terms are not the same. This means that the sequence is not arithmetic.
Now let's determine if the sequence is geometric by checking if there is a common ratio between consecutive terms.
To find the common ratio, we divide each term by its consecutive term:
81 ÷ 3 = 27
3 ÷ (1/9) = 27
As we can see, the ratios between consecutive terms are the same. This means that the sequence is geometric.
So, the correct answer is option B: The sequence is geometric because it decreases by a factor of 1/27.