What number complete the pattern? Note that there is a single algebraic equations ( limited to the basic arithmetic operations of addition, subtraction, multiplication and division) that repeat across all the rows.             2,-3,9,5.                                                       8,?,3,7.                                                          -4,2,4,-6.                                                    5,2,8,1

To determine the missing number, let's analyze the given sequences and search for a repeating algebraic equation involving basic arithmetic operations.

### Given sequences:

1. \( 2, -3, 9, 5 \)
2. \( 8, ?, 3, 7 \)
3. \( -4, 2, 4, -6 \)
4. \( 5, 2, 8, 1 \)

### Step-by-step analysis:

Let's examine each column across the rows to see if there’s a common pattern:

#### First Column: \( 2, 8, -4, 5 \)
Look at the differences:
- \( 8 - 2 = 6 \)
- \( -4 - 8 = -12 \)
- \( 5 - (-4) = 9 \)

There seems to be no consistent arithmetic relationship in the first column, so let's try looking at the other columns.

#### Second Column: \( -3, ?, 2, 2 \)

This column is missing a number, but let's observe other columns first before returning to this.

#### Third Column: \( 9, 3, 4, 8 \)
Look at the differences:
- \( 3 - 9 = -6 \)
- \( 4 - 3 = 1 \)
- \( 8 - 4 = 4 \)

While there is no immediate linear relationship here, let's check the fourth column.

#### Fourth Column: \( 5, 7, -6, 1 \)
Look at the differences:
- \( 7 - 5 = 2 \)
- \( -6 - 7 = -13 \)
- \( 1 - (-6) = 7 \)

Still, no consistent arithmetic pattern is emerging across any of the columns directly. Thus, it’s likely that the algebraic rule involves some operation that combines elements from multiple columns.

#### Hypothesis:
There could be a relationship involving sums or operations between adjacent columns.

To summarize: The analysis above suggests a complex pattern that may not directly follow simple column-wise arithmetic progressions.

Since I need to refine this, let me test

What number complete the pattern? Note that there is a single algebraic equation (limited to the basic arithmetic operations of addition, subtraction, multiplication and division) that repeats across all the rows. 2,-3,9,5. 8,?,3,7. -4,2,4,-6. 5,2,8,1

Learn how to complete the missing number in a repeating arithmetic pattern using basic operations like addition, subtraction, multiplication, and division. This problem covers core arithmetic concepts and is suitable for students in Grades 6-8.

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