Answer:
Sequence B, Sequence A, Sequence C
Explanation:
Data obtained from the question include the following:
Sequence A: 160, 40, 10, 2.5,
Sequence B: -21, 63, -189, 567, ...
Sequence C: 8, 12, 18, 27
Next, we shall determine the common ratio of each sequence. This is illustrated below:
Common ratio (r) is simply obtained by dividing the 2nd term (T2) by the 1st term (T1) or by dividing the 3rd term (T3) by the 2nd term (T2). Mathematically, it is expressed as:
r = T2/T1 = T3/T2
For sequence A:
160, 40, 10, 2.5
2nd term (T2) = 40
Ist term (T1) = 160
Common ratio (r) =..?
r = T2/T1
r = 40/160
r = 1/4
r = 0.25
Therefore, the common ratio is 0.25.
For sequence B:
-21, 63, -189, 567
2nd term (T2) = 63
Ist term (T1) = -21
Common ratio (r) =..?
r = T2/T1
r = 63/-21
r = - 3
Therefore, the common ratio is - 3.
For Sequence C:
8, 12, 18, 27
2nd term (T2) = 12
Ist term (T1) = 8
Common ratio (r) =..?
r = T2/T1
r = 12/8
r = 3/2
r = 1.5
Therefore, the common ratio is 1.5.
Summary:
Sequence >>>>> Common ratio
A >>>>>>>>>>>>> 0.25
B >>>>>>>>>>>>> - 3
C >>>>>>>>>>>>> 1.5
From the above illustration,
Ordering the sequence from least to greatest common ratio, we have:
Sequence B, Sequence A, Sequence C.