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What number completes 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 rows.



To find the missing number represented by the question mark (?), we need to identify a repeating pattern or equation that applies to each row. Let’s analyze each row systematically to identify the rule:

### Row Analysis:

1. **First row:** \(2, -3, 9, 5\)
2. **Second row:** \(8, ?, 3, 7\)
3. **Third row:** \(-4, 2, 4, -6\)
4. **Fourth row:** \(5, 2, 8, 1\)

After examining each row, a common pattern appears: 

**Pattern Analysis:**

The equation that repeats across all rows appears to be:
\[
\text{First number} + \text{Second number} \times \text{Third number} = \text{Fourth number}
\]

Let's check this rule for each row:

1. **First row**:  
   \( 2 + (-3) \times 9 = 2 - 27 = -25 \)  
   This row does not directly fit, which suggests the equation involves more steps.

2. **Second row (with ? as the unknown)**:  
   \( 8 + ? \times 3 = 7 \).  
   Solving for ?:  
   \( 8 + 3x = 7 \).  
   \( 3x = -1 \).  
   \( x = -\frac{1}{3} \).

This suggests that an unusual transformation may be at work.

Would you like more detail on this pattern exploration or tips on finding an unknown in sequences?


Explore how to identify patterns in arithmetic sequences to solve for missing numbers. This problem involves analyzing a sequence with a repeating algebraic equation. Suitable for students in Grades 7-9.

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