Answered

Which of the following sequences are geometric?

Check all that apply.

A6, 18, 54, 162, 486
B2, 3, 5, 8, 13, 21
C2, 5, 8, 11, 14, 17
D-4, -2, -1, -0.5, -0.25, -0.125

Verified Answer :

jtvatsim

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? 
63 = 18
183 = 54
543 = 162
1623 = 486
Yes! We are multiplying by 3 each time. This is a geometric sequence!

[B] Are we multiplying by the same thing?
23/2 = 3
33/2 = 9/2 which is not 5.
NOPE

[C] Are we multiplying by the same thing?
25/2 = 5
55/2 = 25/2 which is not 8
NOPE

[D] Are we multiplying by the same thing?
-41/2 = -2
-21/2 = -1
-11/2 = -0.5
-0.51/2 = -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

\(\rm r = \dfrac{18}{6} = \dfrac{54}{18} = \dfrac{162}{54} = \dfrac{486}{162} = 3\)

The sequence is a geometric sequence.

B. 2, 3, 5, 8, 13, 21, then the common ratio will be

\(\rm r = \dfrac{3}{2} eq \dfrac{5}{3} eq \dfrac{8}{5} eq \dfrac{13}{8} eq \dfrac{21}{13}\)

The sequence is not a geometric sequence.

C. 2, 5, 8, 11, 14, 17, then the common ratio will be

\(\rm r = \dfrac{5}{2} eq \dfrac{8}{5} eq \dfrac{11}{8} eq \dfrac{14}{11} eq \dfrac{17}{14}\)

The sequence is not a geometric sequence.

D. -4, -2, -1, -0.5, -0.25, -0.125, then the common ratio will be

\(\rm r = \dfrac{-4}{-2} = \dfrac{-2}{-1} = \dfrac{-1}{-0.5} = \dfrac{-0.5}{-0.25} = \dfrac{-0.25}{-0.125} = 2\)

The sequence is a geometric sequence.

More about the sequence link is given below.

https://brainly.com/question/21961097

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