Three geometric sequences are given below.Sequence A: 160, 40, 10, 2.5, . . .Sequence B: -21, 63, -189, 567, . . .Sequence C: 8, 12, 18, 27, . . . Order the sequences from least common ratio to greatest common ratio.
To order the sequences from least common ratio to greatest common ratio, we need to calculate the common ratio for each sequence first
To order the sequences from least common ratio to greatest common ratio, we need to calculate the common ratio for each sequence first.
The common ratio (r) of a geometric sequence can be found by dividing any term (except the first term) by its preceding term.
For Sequence A:
r = 40/160 = 1/4 = 0.25
For Sequence B:
r = 63/-21 = -3
For Sequence C:
r = 12/8 = 3/2 = 1.5
Now, let’s organize the sequences based on the magnitude of the common ratio:
Least Common Ratio:
– Sequence B with a common ratio of -3.
Intermediate Common Ratio:
– Sequence A with a common ratio of 0.25.
Greatest Common Ratio:
– Sequence C with a common ratio of 1.5.
Therefore, the sequences can be ordered from least common ratio to greatest common ratio as follows:
Sequence B < Sequence A < Sequence C
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