Question

Franklin found some empty bins to put cans into for recycling. He put 11 empty cans in the first bin, 44 empty cans in the second bin, 176 empty cans in the third bin, and 704 empty cans in the fourth bin. What kind of sequence is this?

Answer 1

To determine the type of sequence that Franklin's cans form, let's look at the number of cans in each bin:

- First bin: 11 cans
- Second bin: 44 cans
- Third bin: 176 cans
- Fourth bin: 704 cans

Now, let's analyze the ratios of consecutive terms:

1. From the 1st to the 2nd bin:
\[
\frac{44}{11} = 4
\]

2. From the 2nd to the 3rd bin:
\[
\frac{176}{44} = 4
\]

3. From the 3rd to the 4th bin:
\[
\frac{704}{176} = 4
\]

Since the ratio of each term to the previous term is the same (each term is multiplied by 4 to get the next term), this indicates that the sequence is a geometric sequence with a common ratio of 4.

Thus, the sequence formed by the number of cans in the bins is a geometric sequence.