Question

Which is a geometric sequence
12,24,36,48,60
100,200,300,400,500
9;81;729;6,561
3;36;432;5,184

Answer 1

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant factor, known as the common ratio.

Let's analyze each of the provided sequences to determine if any of them are geometric:

1. **12, 24, 36, 48, 60**
- Ratios: 24/12 = 2, 36/24 = 1.5, 48/36 = 1.33, 60/48 = 1.25
- This is **not** a geometric sequence because the ratios are not constant.

2. **100, 200, 300, 400, 500**
- Ratios: 200/100 = 2, 300/200 = 1.5, 400/300 = 1.33, 500/400 = 1.25
- This is **not** a geometric sequence because the ratios are not constant.

3. **9, 81, 729, 6,561**
- Ratios: 81/9 = 9, 729/81 = 9, 6,561/729 = 9
- This **is** a geometric sequence with a common ratio of 9.

4. **3, 36, 432, 5,184**
- Ratios: 36/3 = 12, 432/36 = 12, 5,184/432 = 12
- This **is** a geometric sequence with a common ratio of 12.

In summary, both the third sequence (9, 81, 729, 6,561) and the fourth sequence (3, 36, 432, 5,184) are geometric sequences.