Question

which of the following are geometric sequences?
A.) 5, 10, 20, 40 , 80, 160
B.) 3, 6, 9, 12, 15,18
C.) 10, 5, 2.5, 1.25, 0.625, 0.1325
D.) 1,3, 9, 27, 81

Answer 1

i got A and D but idk if that is the only one

Answer 2

?

Answer 3

"In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio"

So if you can multiply the numbers by the same multiplier each time to get the next, then it is considered geometric.

Starting with choice A:
5 times 2 = 10. So we'll test 2 as a common multiplier. 5*2 = 10 * 2 = 20 * 2 = 40 * 2 = 80 * 2 = 160
Since each successive number is just the previous number multiplied by 2, then A is a geometric sequence.

With B, 3 times 2 = 6. So we'll once again test 2 as a multiple. 3 * 2 = 6 * 2 = 12.. 12=/=9 therefore it is not geometric.

With C, 10 * 1/2 = 5 so we'll test 1/2 as the multiple.
10 * 1/2 = 5 * 1/2 = 2.5 * 1/2 = 1.25 * 1/2 = .0625 * 1/2 = .1325
It is therefore geometric.

and I'm not going to show it out (it seems like you already did D), but D is also geometric!