Question

Which of the following graphs could be a representation of a geometric sequence?

Check all that apply.

Answer 1

is that all of them?

Answer 2

Yeah

Answer 3

okay so we know that a geometric sequence will increase/decrease by a common ratio, right?

Answer 4

Yep

Answer 5

okay, so if each x value cause the y values to change by a factor, it can't be linear like B.

Answer 6

aha

Answer 7

so B is not going to be checked

Answer 8

as for the others do any of them look like they change at a constant ratio?

Answer 9

like each y value is related to the one before it in a direct ratio

Answer 10

A?

Answer 11

in the graph of A, you start with what looks like y=3, when it gets to x=1, the \[y \approx 9\]

Answer 12

now compare this ration of 3:9 to the next step up of what look like y=27

Answer 13

is a 3:9 ratio equal to a 9:7 ratio?

Answer 14

sorry, 27

Answer 15

this is all you have to do with all the possible answers

Answer 16

let x go in steps of 1. x = 0, 1, 2, ...
Find the corresponding y.
For graph A, y goes: 3, 9, 27, ...
(y goes up by the SAME factor of 3 each time. So 3 is the common ratio).
Therefore, graph A is a geometric sequence.

B cannot be a geometric sequence because it is a straight line which is a linear relationship.

How about C?

Answer 17

I believe it is as well

Answer 18

Correct. What is the common ratio for C?

Answer 19

not sure

Answer 20

In graph C, as x goes 0, 1, 2 what are the corresponding values of y?

Answer 21

y goes 5, 2.5, 1.25, ....
Each time the y-value is getting divided by 2.
So the common ratio is 1/2 or 0.5 and C) is a geometric sequence.

Answer 22

So only A and C?