Question

Which of the following sequences are geometric sequences?

Check all that apply.

A. 10, 13, 16.9, 21.97, 28.561, 37.1293, ...
B. 10, 12, 13.1, 13.31, 15.641, ...
C. 15, 30, 60, 120, 240, ...
D. 0.1, 0.01, 0.001, 0.0001, 0.00001, ...
E. 5, 125, 225, 1,625, 3,125, ...

Answer 1

can you define geometric sequences for me?

Answer 2

Yes, it's a sequence of numbers where each term is multiplied by the same value each time? But, I'm having a hard time piecing it all together.

Answer 3

Can the number be a fraction or decimal?

Answer 4

let me give you an example of a geometric sequence: 2,6,18,34 is a geometric ratio with common ratio 3.

Answer 5

2*3=6, 6*3=18, 18*3=34, etc.

Answer 6

another example of a geometric sequence is 10, 5, 2.5, 1.25....

Answer 7

the common ratio is 1/2

Answer 8

so to answer your question above, the number can be a decimal

Answer 9

Oh! I think I get it now, your examples make sense. Would the answers be A, C, and D? I really can't afford to get this wrong.

Answer 10

for A. the common ration is 1.3, that means that it is indeed a common ratio. Now, can you provide me the reasoning for the other two?

Answer 11

@Ashlyn1634

Answer 12

geometric sequence or series take the form

ar^0+ar^1+ar^2+...ar^n

1 2 3 nth term

Answer 13

right the general form of a geometric sequence is a+ar+ar^2+ar^3+ar^4+....
a represents the scale factor, and r represents the common ratio \[r \neq0\]

Answer 14

Oh, the next would be a common ratio of 2 because 15,30, 60, 120 follow the sequence. And since the decimal would need to get smaller by 1 zero, you'd multiply it by .1 which would equal 0.1, 0.01, 0.001, 0.0001, and 0.00001.

Answer 15

thats right, so A, C, D are all geometric ratios. Just to make sure you understand, can you prove to me why B and E. aren't?

Answer 16

10, 12, 13.1, 13.31, and 15.641 don't have the same ratio because 10-12 would be 1.2 while the rest all have different ratios and are just kind of a jumbled mess. 5, 125, 225, 1,625, 3,125 are all multiples of 5, but they 5-125 would have a ratio of 25, while the rest have ratios of different variations.

Answer 17

niceee im glad you understand now kudos! :D

Answer 18

that totes deserved a medal ;)

Answer 19

Thank you, that was very helpful. Thanks for not just telling me the answer and actually teaching me. It's better now that I've learned. I can do my quiz now! Thanks again.

Answer 20

@Directrix look i have the whole giving the process stuff down :D