U3 L10 Connections 7th grade
4. What explains why the sequence 216, 12, 2/3, ... is arithmetic or geometric.
A. The sequence is geometric because it decreases by a factor of 6
B. The sequence is arithmetic because it decreases by a factor of 6
C. The sequence is geometric because it decreases by a factor of 1/18
D. The sequence is arithmetic because it decreases by a factor of 1/18
A geometric sequence is a sequence in which the next or previous numbers are arrived at by multiplying by a number. An arithmetic sequence is a sequence in which the next or previous numbers are arrived at by adding a number. since 216 times 1/18 is 12 and 12 times 1/18 is 2/3, this is a geometric sequence decreasing by a factor of 1/18. c is correct.
I think it is c
To determine whether the given sequence 216, 12, 2/3, ... is arithmetic or geometric, we need to examine the pattern of the sequence and identify whether it follows the rules of an arithmetic or geometric sequence.
An arithmetic sequence is characterized by a common difference between consecutive terms, meaning that each term is obtained by adding or subtracting the same fixed value.
A geometric sequence is characterized by a common ratio between consecutive terms, meaning that each term is obtained by multiplying or dividing the previous term by the same fixed value.
Let's examine the given sequence:
216, 12, 2/3, ...
To determine if this sequence is arithmetic, we would need to find a common difference between consecutive terms. However, it is not possible to identify a fixed value that we add or subtract to obtain the next term. Therefore, the sequence is not arithmetic.
To determine if this sequence is geometric, we would need to find a common ratio between consecutive terms. We can divide each term by its previous term to see if there is a consistent ratio:
12 / 216 = 1/18
(2/3) / 12 = 1/18
As we can see, each term is obtained by multiplying the previous term by 1/18. Thus, the sequence follows a consistent pattern, making it a geometric sequence.
Given these observations, the correct option is:
C. The sequence is geometric because it decreases by a factor of 1/18.