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 ratios for each sequence
To order the sequences from least common ratio to greatest common ratio, we need to calculate the common ratios for each sequence.
The common ratio (r) of a geometric sequence is found by dividing any term in the sequence by its preceding term. Let’s calculate the common ratios for each sequence:
Sequence A:
Common ratio (r) = 40/160 = 0.25
Since the common ratio is less than 1, it is a decreasing sequence.
Sequence B:
Common ratio (r) = 63/-21 = -3
Since the common ratio is less than 1 and negative, it is a decreasing sequence.
Sequence C:
Common ratio (r) = 12/8 = 1.5
Since the common ratio is greater than 1, it is an increasing sequence.
Now that we have calculated the common ratios for each sequence, we can order them from least to greatest:
Sequence B: -3
Sequence A: 0.25
Sequence C: 1.5
Therefore, the sequences, from least common ratio to greatest common ratio, are: Sequence B, Sequence A, Sequence C.
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