1 Which sequence is geometric?

geometric means

... that a term is multiplied by some value (the ratio) to get the next term

thank you.

To determine which sequence is geometric, we need to check if there is a common ratio between consecutive terms. A geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a fixed, non-zero number.

Let's analyze each options:

Option A: 3, 6, 9, 12...
To check if this sequence is geometric, we calculate the ratio of consecutive terms:
6/3 = 2
9/6 = 1.5
12/9 = 1.33...

The ratios are not the same, so this sequence is not geometric.

Option B: 5, 6, 8, 11...
Calculating the ratios:
6/5 = 1.2
8/6 = 1.33...
11/8 = 1.375

The ratios are not consistent, so this sequence is not geometric.

Option C: 3, 5, 7, 9...
Calculating the ratios:
5/3 = 1.67...
7/5 = 1.4
9/7 = 1.29...

Again, the ratios are not consistent, so this sequence is not geometric.

Option D: 2, 6, 18, 54...
Calculating the ratios:
6/2 = 3
18/6 = 3
54/18 = 3

The ratios are all consistent at 3, so this sequence is geometric.

Therefore, the answer is Option D.