Let's carefully analyze the pattern in the number of rocks Matt put in each box:
1. In the first box, Matt put 1 rock.
2. In the second box, he put 3 rocks.
3. In the third box, he put 9 rocks.
4. In the fourth box, he put 27 rocks.
We can observe the sequence of numbers: 1, 3, 9, 27. By looking at the progression, we see that each number is three times the previous number. This indicates a geometric progression where the common ratio is 3.
To find the number of rocks in each subsequent box, we multiply the number of rocks in the current box by 3.
Let's verify this:
- Number of rocks in the second box = [tex]\(1 \times 3 = 3\)[/tex]
- Number of rocks in the third box = [tex]\(3 \times 3 = 9\)[/tex]
- Number of rocks in the fourth box = [tex]\(9 \times 3 = 27\)[/tex]
Following this pattern, we can determine the number of rocks in the fifth box:
- Number of rocks in the fifth box = [tex]\(27 \times 3\)[/tex]
Now, perform the multiplication:
[tex]\[ 27 \times 3 = 81 \][/tex]
So, Matt put 81 rocks in the fifth box.
