Respuesta :
Let's start by first remembering what a "geometric sequence" is. A geometric sequence is a sequence of numbers that multiply by the same number each time. For example,
2, 4, 8, 16
is a geometric sequence since each number is multiplied by 2 from one to the next, but
2, 4, 6, 8
is NOT a geometric sequence. We are adding 2 each time, but not multiplying, so it doesn't count. We have to be multiplying to have a geometric sequence.
[A] Let's look at A, are we multiplying by the same thing?
6*3 = 18
18*3 = 54
54*3 = 162
162*3 = 486
Yes! We are multiplying by 3 each time. This is a geometric sequence!
[B] Are we multiplying by the same thing?
2*3/2 = 3
3*3/2 = 9/2 which is not 5.
NOPE
[C] Are we multiplying by the same thing?
2*5/2 = 5
5*5/2 = 25/2 which is not 8
NOPE
[D] Are we multiplying by the same thing?
-4*1/2 = -2
-2*1/2 = -1
-1*1/2 = -0.5
-0.5*1/2 = -0.25
-0.25*1/2 = -0.125
Yep, we are multiplying by 1/2 each time! This is a geometric sequence!
2, 4, 8, 16
is a geometric sequence since each number is multiplied by 2 from one to the next, but
2, 4, 6, 8
is NOT a geometric sequence. We are adding 2 each time, but not multiplying, so it doesn't count. We have to be multiplying to have a geometric sequence.
[A] Let's look at A, are we multiplying by the same thing?
6*3 = 18
18*3 = 54
54*3 = 162
162*3 = 486
Yes! We are multiplying by 3 each time. This is a geometric sequence!
[B] Are we multiplying by the same thing?
2*3/2 = 3
3*3/2 = 9/2 which is not 5.
NOPE
[C] Are we multiplying by the same thing?
2*5/2 = 5
5*5/2 = 25/2 which is not 8
NOPE
[D] Are we multiplying by the same thing?
-4*1/2 = -2
-2*1/2 = -1
-1*1/2 = -0.5
-0.5*1/2 = -0.25
-0.25*1/2 = -0.125
Yep, we are multiplying by 1/2 each time! This is a geometric sequence!
If the common ratio between the two successive terms must be constant. Then sequence A and sequence D are the geometric sequence.
What is a sequence?
A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
If the common ratio between the two successive terms must be constant. Then the sequence is called a geometric sequence.
The sequences are given below.
A. 6, 18, 54, 162, 486, then the common ratio will be
[tex]\rm r = \dfrac{18}{6} = \dfrac{54}{18} = \dfrac{162}{54} = \dfrac{486}{162} = 3[/tex]
The sequence is a geometric sequence.
B. 2, 3, 5, 8, 13, 21, then the common ratio will be
[tex]\rm r = \dfrac{3}{2} \neq \dfrac{5}{3} \neq \dfrac{8}{5} \neq \dfrac{13}{8} \neq \dfrac{21}{13}[/tex]
The sequence is not a geometric sequence.
C. 2, 5, 8, 11, 14, 17, then the common ratio will be
[tex]\rm r = \dfrac{5}{2} \neq \dfrac{8}{5} \neq \dfrac{11}{8} \neq \dfrac{14}{11} \neq \dfrac{17}{14}[/tex]
The sequence is not a geometric sequence.
D. -4, -2, -1, -0.5, -0.25, -0.125, then the common ratio will be
[tex]\rm r = \dfrac{-4}{-2} = \dfrac{-2}{-1} = \dfrac{-1}{-0.5} = \dfrac{-0.5}{-0.25} = \dfrac{-0.25}{-0.125} = 2[/tex]
The sequence is a geometric sequence.
More about the sequence link is given below.
https://brainly.com/question/21961097
#SPJ2
