Identify the sequence...
3,888, 216, 12, 2/3...
a. arithmetic
b. geometric
c. neither
d. both
Is it c or d?
It is hard to tell sometimes, but an arithmetic sequence would have the same number added or subtracted. That doesn't seem to be the case.
A could way to check for a geometric sequence is to divide the first number by the second. I divided 3888 by 216 and got 18.
Next try to divide to 216 by 18 to see if the answer is 12.
Finally divide 12 by 18 to see if the answer is 2/3.
If they work out, then you have a geometric sequence.
The given sequence is:
3,888, 216, 12, 2/3...
To determine whether this sequence is arithmetic, geometric, both, or neither, we can analyze the pattern:
If we divide each term by the previous term, we get:
216 / 3,888 ≈ 0.0556
12 / 216 ≈ 0.0556
2/3 / 12 ≈ 0.0556
The ratios between successive terms are approximately the same, which indicates that the sequence is geometric.
Therefore, the answer is:
b. geometric
To identify the sequence, we need to determine if the numbers are following a specific pattern.
In this sequence, if we look at the differences between consecutive terms, we get:
216 - 3,888 = -3,672
12 - 216 = -204
(2/3 - 12) = -35/3
Since the differences are not constant, we can conclude that the sequence is not an arithmetic sequence.
Next, let's look at the ratios between consecutive terms:
216 / 3,888 ≈ 0.0556
12 / 216 ≈ 0.0556
(2/3) / 12 ≈ 0.0556
The ratios are all approximately equal to 0.0556. Since the ratios are constant, we can conclude that the sequence is a geometric sequence.
Therefore, the correct answer is:
b. geometric