Question

Which of the following sequences are geometric?

A. -4, -2, -1, -0.5, -0.25, -0.125
B. 2, 3, 5, 8, 13, 21
C. 2, 5, 8, 11, 14, 17
D. 6, 18, 54, 162, 486

Answer 1

See if they have a common ratio.
Divide first term by second term. Is that the same when second term is divide by third term? Third by fourth? If yes, then it is a geometric sequence. If not, then it is not.

Answer 2

okay, so D is a possible answer right?

Answer 3

You can reverse the order of division too.
2nd term / 1st term = 3rd term / 2nd term = 4th term / 3rd term = r
Or
1st term / 2nd term = 2n term / 3rd term = 3rd term / 4th term = r

Answer 4

Yes, D is a geometric sequence.

Answer 5

doing the math it doesnt seem like the other 3 are possible answers. am i missing something or is that correct?

Answer 6

Try A again.

Answer 7

Oh, would A be correct because it increases by .25 each time?

Answer 8

not "increases by .25"

The common ratio is 1/2. Just multiply each term by 1/2 and you will get the next term.

Answer 9

Geometric Sequence goes like: a, ar, ar^2, ar^3, ar^4, ......

Answer 10

Where \(a\) is the starting term and \(r\) is the common ratio

Answer 11

In case A) a= -4 and r = 1/2

Answer 12

and in case D) a=6 and r=3

Answer 13

You multiply each term by the same constant (called the common ratio) and you will get the next term.

Answer 14

case D)
6
6*3 = 18
18*3 = 54
54*3 = 162
162*3 = 486

Answer 15

oh that completely makes sense! for some reason I was thinking of something totally different. thank you both! :)

Answer 16

you are welcome.

Answer 17

no problem :)