To find the missing number in the pattern, we should first analyze the existing rows of numbers to identify the relationships between the elements.
Let's look at each row to uncover any patterns:
### Row 1: [tex]\([6, -5, -6, 5]\)[/tex]
- [tex]\(6 - 11 = -5\)[/tex]
- [tex]\(-5 - 1 = -6\)[/tex]
- [tex]\(-6 + 11 = 5\)[/tex]
### Row 2: [tex]\([-4, 3, 2, -6]\)[/tex]
- [tex]\(-4 + 7 = 3\)[/tex]
- [tex]\(3 - 1 = 2\)[/tex]
- [tex]\(2 - 8 = -6\)[/tex]
### Row 3: [tex]\([6, 6, 9, 4]\)[/tex]
- [tex]\(6 + 0 = 6\)[/tex]
- [tex]\(6 + 3 = 9\)[/tex]
- [tex]\(9 - 5 = 4\)[/tex]
Now, let's determine the pattern in the fourth row where the second number is missing:
### Row 4: [tex]\([-9, ?, 6, 3]\)[/tex]
We know the relationships:
- The first element is -9.
- The second element should satisfy the pattern which involves simple arithmetic operations.
Since we need to solve for the missing number based on the previous numbers' patterns, we notice in the sequences analyzed that every third column’s calculation improves on the number sequences provided. We focus on those transitions.
From similar observed patterns in the third row, we derive:
- [tex]\(-9 + x\)[/tex]
For the pattern to be consistent from previously seen operations in other rows, we use the observed largest number sequence:
- [tex]\(-9 + 15 = 6\)[/tex]
Thus, solving for [tex]\(x\)[/tex]:
- [tex]\(-9 + 15 = 6\)[/tex]
Hence, the missing number in the fourth row is:
[tex]\[ x = 15 \][/tex]
This gives us the completed pattern as:
[tex]\[ [-9, 15, 6, 3] \][/tex]
The number that completes the pattern is [tex]\( \boxed{15} \)[/tex].
