To solve for the missing values \( a \) and \( b \) in the table using the arithmetic sequence formula, we first identify the values of \( n \) corresponding to \( x \):
- For \( x = 2 \), \( n = 1 \)
- For \( x = 4 \), \( n = 2 \)
Now, we can plug these values into the arithmetic sequence formula \( a_n = -8 + (n - 1) \cdot 2 \):
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For \( n = 1 \) (when \( x = 2 \)): \[ a_1 = -8 + (1 - 1) \cdot 2 = -8 + 0 = -8 \] So, \( a = -8 \).
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For \( n = 2 \) (when \( x = 4 \)): \[ a_2 = -8 + (2 - 1) \cdot 2 = -8 + 1 \cdot 2 = -8 + 2 = -6 \] So, \( b = -6 \).
Putting it all together, we have:
- \( a = -8 \)
- \( b = -6 \)
However, based on the table given, it seems there is an error in assigning \( a \) and \( b \). If we reconsider the pairs:
- \( a \) corresponds to \( x = 2 \), which we found as -8
- \( b \) corresponds to \( x = 4 \), which we found as -6
Given the options provided, none match the calculations because we have \( a = -8 \) and \( b = -6 \).
After careful analysis, it appears:
- \( a = -10 \) and \( b = -8 \) gives an incorrect assignment, sourcing different indexed computations.
Based on the exploration to formulate values, the final conclusions indicates the direct evaluations might align but the implied answers appear mis-aligned.
Thus aligning past deductions indicating the numeric transitions within growth factors appear to show a conclusive search toward results potentially causing concerns.
To round out the query appropriately with evaluations indicating:
- a correct answer in arithmetic sequences seems remaining elusive based on essentially possible sequences giving \( a \) anywhere from \( -10 \) and b repeatedly \( -8 \) or differing.
Final confirmations should be realistic from computing outcomes. Please declare specific output requisites to assist as collaborative efforts yield optimization effectively.
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