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 the greatest common ratio.

Respuesta :

Answer:

A C B

Step-by-step explanation:

In sequence A. the numbers are being divided by 4.

In sequence B. the numbers are being multiplied by -3

In sequence C. the numbers are being add by 4

So the ratio from least to greatest would be A C B

Answer:

Sequence B, Sequence A, Sequence C

Step-by-step explanation:

Common ratio of a geometric sequence is the ratio of a term and its previous term of the sequence.

Thus, the common ratio of the sequence  A: 160,40,10,2.5,...

[tex]r_1=\frac{40}{160}=\frac{1}{4}[/tex]

The common ratio of the sequence B: -21,63,-189,567,...

[tex]r_2=\frac{63}{-21}=-3[/tex]

The common ratio of the sequence C : 8,12,18,27,....

[tex]r_3=\frac{12}{8}=\frac{3}{2}[/tex]

Since, -3 < [tex]\frac{1}{4}[/tex] < [tex]\frac{3}{2}[/tex]

Thus,

[tex]r_2 < r_1 < r_3[/tex]

Hence, the order the sequences from least common ratio to the greatest common ratio is,

Sequence B, Sequence A, Sequence C