Question

Stefan found some empty bins to put cans into for recycling. He put 11 empty cans in the first bin, 33 empty cans in the second bin, 99 empty cans in the third bin, and 297 empty cans in the fourth bin. What kind of sequence is this?

Answer 1

The sequence of the number of cans in each bin is as follows:

1. First bin: 11
2. Second bin: 33
3. Third bin: 99
4. Fourth bin: 297

To analyze this sequence, let's look at the relationship between consecutive terms:

- From the first bin to the second bin: \( 33 \div 11 = 3 \)
- From the second bin to the third bin: \( 99 \div 33 = 3 \)
- From the third bin to the fourth bin: \( 297 \div 99 = 3 \)

Each term is obtained by multiplying the previous term by 3. This indicates that the sequence is a geometric sequence with a common ratio of 3.

To summarize, the sequence \( 11, 33, 99, 297 \) is a geometric sequence where each term is obtained by multiplying the previous term by 3.